(a) To construct the cash -flow for the 7 years. [600384]

Question one
(a) To construct the cash -flow for the 7 years.

THE CASHFLOW FOR 7 YEARS OF ASSESSING PROJECT VIABILITY
item/year O 1 2 3 4 5 6 7
cash outflow
000,000"
fixed capital 1500
fixed machinery 200
working capital 30 15 20 28 13 10 10
financing cost 30 30 22 20 20
Total
outflow(cost) 200 1530 15 50 58 35 30 30

Revenue 0 250 300 360 432 518.4 622.08 746.496
sale of fixed
capital 400
sale of working
asset 80
sale of fixed
machinery 20
TOATL
INFLOW(BENEFIT) 0 250 300 360 432 518.4 622.08 1246.496
NET NEBEFIT -200 -1280 285 310 374 483.4 592.08 1216.496
(b). Calculate the NPV and BC Ratio at 15% discount rate

Year BENEFIT COST DISCOUNT FACTOR
(15%) DISCOUNT
BENEFIT DISC OUNT .COS T PRESENT VALUE
0 0 200 1 0 200 -200
1 250 1530 0.87 217.5 1331.1 -1113.6
2 300 15 0.756 226.8 11.34 215.46
3 360 50 0.658 236.88 32.9 203.98
4 432 58 0.572 247.104 33.176 213.928
5 518.4 35 0.497 257.6448 17.395 240.249 8
6 622.08 30 0.432 268.73856 12.96 255.7786
7 1246.496 30 0.376 468.682496 11.28 457.4025
TOTAL 1923.349856 1650.151 273.1989
NPV=∑DB -∑DC
Where DB=Discounted benefit
DC=Discounted cost

NPV= 1923.349856 -1650.151 =273.1989
BCR=

BCR=
=1.165

(c) What is the IRR of this project?

IRR=R 1+ (R 2-R1) NPV 1
NPV 1 + NPV 2

Where R 1-Interest rest rate for positive NPV 1
R2-Interest rate for negative NPV 2
Assuming R 2= 25%
Year Discounted
factor Discounted
Benefit Discounted
Cost Discount benefit -Discount cost
0 1 0 200 -200
1 0.8 200 1224 -1024
2 0.64 192 9.6 182.4
3 0.512 184.32 25.6 158.72
4 0.409 176.688 23.722 152.966
5 0.328 170.0352 11.48 158.5552
6 0.262 162.985 7.86 155.125
7 0.209 260.5177 6.27 254.2477
Total -161.986

IRR=0.15 + (0.25 -0.15) 273.1989 =21.27%
273.1989 + -161.986

0.2127776607 x100%= 21.27 %

D/ The investment is worthwhile to be undertaken due to the fact that its NPV is positive which is
273.1989 and its benefit cost ratio is greater than one 1.2 and its internal rate of return is greater than
the opportunity cost of capital.
E/ It is was nec essary to assess the internal rate of return so as identify at which rate of return the
investment will break -even that means where total cost is equal to total revenue and NPV=0
Question 2 solution
(i) draw a network diagram,
O, 6
J, 11

F, 6 N, 2

G, 2
M, 8
B, 12 E, 7 L, 3
A,2
K, 1
C, 6 I, 10

D, 4
H, 2

Critical path = A B E I L O

(iv) along the critical path, crush
one critical activity by two weeks, do you have a new critical path? If yes sho w the activities along the
path.
0 0
2 2

14 14
21 21
31 31
34 34
40 40
22 24
30 32
20 22
8 25
12 29

J, 11 Q,6

F, 6 N,2
G, 2

B, 10 M, 8
E, 7 L, 3
A, 2

K,1
C, 6

I, 10

D, 4

H, 2

ANSWER There is no new critical path when you crush one critical activity by two weeks.

0 0
20 22
29 29
28 30
12 12
2 2
19 19
28 20
8 23
12 27
32 32
38 38

Question 4

F,2

E, 3

H, 10
A, 5
D, 4

C, 4 I, 2

B, 2

J, 5

G, 14

L, 4
K, 2

M, 1

N, 2

Key
activity
Event

E=earliest event time
L=Latest event time
11 11
1313
8 8
23 23
30 30
25 25
34 34
36 36
2 16
32 33
0 0
4 4
EL
LL

EET=LET=Critical path C -D-E-F-H-I-J-L-N. Critical activity C , D, E, F, H, I, J, L, N
7. Two projects A and B are to be evaluated at 12% interest rate. Project A, cash flow in year 0 is –
10,000 and cash flow in year 1 is 20,000. Project B cash flow in -50,000 in year 0 and cash flow in year 1
is 75,000. Which th e best project to accept? Why?
SOLUTION
PROJECT A
Cash flow in year 0 is – 10,000
Cash flow in year 1 is 20,000
Project B
Cash flow in year 0 is -50,000
Cash flow in year 1 is 75,000
Interest rate is 12% in both projects
Year project
A Project
B Discount
factor Discount project A Discounted project
B
0 -10000 -50000 1 -10000 -50000
1 20000 75000 0.893 17860 66975
NPV 7860 16975
NPV=16975 for project B
NPV= 7860 for project A
BCR=

BCR for project A=
=1.786
BCR for project B=
=1.33
Project B is worthwhile to undertake than project A due to the fact that net present value
of project B is greater than net present value of project A

8. (i) Determine project acceptability by using
Show the ranking of projects by each of the three methods
Year Project
A Project
B Project
C Discount
factor 10% Discounted
project A Discounted
project B Discounted
project C
0 -500000 -500000 –
500000 1 -500000 -500000 -500000
1 90,000 70000 200,000 0.909090909 81818.18182 63636.36364 181818.1818
2 90,000 80000 200,000 0.826446281 74380.16529 66115.70248 165289.2562
3 90,000 90000 200,000 0.751314801 67618.33208 67618.33208 150262.9602
4 90,000 100000 100,000 0.683013455 61471.21098 68301.34554 68301.34554
5 90,000 110000 0.620921323 55882.91908 68301.34554 0
6 90,000 120000 0.56447393 50802.6537 67736.87161 0
7 90,000 130000 0.513158118 46184.23064 66710.55537 0
8 90,000 140000 0.46650738 41985.66422 65311.03323 0
9 90,000 150000 0.424097618 38168.78565 63614.64276 0
10 90,000 160000 0.385543289 34698.89605 61686.92631 0
NPV 53011.03951 159033.1185 65671.74373
BCR of p roject A=
=1.11
BCR of project B=

BCR of project C =

Ranking by using net present value
Project NPV Ranking
A 53011.03951 2
B 159033.1185 3
C 65671.74373 1
Ranking by using payback period
Project Payback period Ranking
A 5.6 years 3
B 5.4 years 2
C 2.5 years 1
Ranking by using benefit cost ratio.
Project Benefit cost ratio Ranking
A 1.11 3
B 1.32 1
C 1.13 2

QUESTION 9
YEARS B.Sc. M.Sc. discount
factors
10% Discount
factor B.Sc. Discount factor for
M.Sc.
1 15,000,000 -15,000,000 0.909091 13636363.6 -13636363.6
2 15,000,000 -15,000,000 0.826446 12396694.2 -12396694.2
3 15,000,000 50,000,000 0.751315 11269722 37565740.05
4 20,000,000 50,000,000 0.683013 13660269.1 34150672.77
5 20,000,000 50,000,000 0.620921 12418426.5 31046066.15
6 20,000,000 50,000,000 0.564474 11289478.6 28223696.5
7 50,000,000 50,000,000 0.513158 25657905.9 25657905.91
NPV 100328860 130611023.5

You should opt to go to for M.Sc. soon after your B.Sc. because net benefit value for going for M.Sc. is
greater than the net benefit value ( NPV )for B.Sc. NPV for M.Sc.is 130611023.5 and NPV for
B.Sc.=100328860
10.

(Iii) Rank the project acceptability by using (a) NPV, (b) BCR, (c) discounted PBP

YEARS/PROJECT PRO A PRO B PRO C PRO D PRO E DISC
FACTOR 10% DISC PR
A DISC PR
B DIS PR C DIC PR D DIS PRO E
0 -1,000,000 -80,000 –
75,000 -50,000 -80,000 1 –
1000000 -80000 -75000 -50000 -80000
1 20,000 30,000 15,000 0.909091 0 18181.82 27272.73 13636.36 0
2 30,000 30,000 15,000 35,000 0.826446 0 24793.39 24793.39 12396.69 28925.62
3 40,000 30,000 15,000 35,000 0.751315 0 30052.59 22539.44 11269.72 26296.02
4 30,000 30,000 15,000 35,000 0.683013 0 20490.4 20490.4 10245.2 23905.47
5 20,000 30,000 15,000 35,000 0.620921 0 12418.43 18627.64 9313.82 21732.25
6 -10,000 15,000 35,000 0.564474 0 -5644.74 0 8467.109 19756.59
7 15,000 35,000 0.513158 0 0 0 7697.372 17960.53
8 3,000,000 15,000 35,000 0.466507 1399522 0 0 6997.611 16327.76
NPV 399522.1 20291.89 38723.6 30023.89 74904.24
(i) Rank the project acceptability by using (a) NPV, (b) BCR, (c) discounted PBP,
Ranking by using net present value
PROJECT NPV RANKING
A 399522.14 1
B 20291.889 5
C 38723.603 3
D 30023.893 4
E 74904.235 2
Ranking by using benefit cost ratio
PROJECT BCR RANKING
A 1.399522141 4
B 1.253648618 5
C 1.516314708 3
D 1.600477859 2
E 1.936302939 1

Ranking by using payback period
PROJECT PBP RANKING
A 8 Years 5
B 3.34 Years 2
C 3.02 Years 1
D 4.26 Years 4
E 4.04 Year 3

(iv) Rank the projects based on their sensitivity level
Let assume interest rate be 20%
years/project Project A Project B Project
C Project D Project E Didcount
factor
20% Discount
project A Discount
project B Discount
project C Discount
project D Discount
project E
0 -1,000,000 -80,000 –
75,000 -50,000 -80,000 1 –
1000000 -80000 -75000 -50000 -80000
1 20,000 30,000 15,000 0.833333 0 16666.67 25000 12500 0
2 30,000 30,000 15,000 35,000 0.694444 0 20833.33 20833.33 10416.67 24305.56
3 40,000 30,000 15,000 35,000 0.578704 0 23148.15 17361.11 8680.556 20254.63
4 30,000 30,000 15,000 35,000 0.482253 0 14467.59 14467.59 7233.796 16878.86
5 20,000 30,000 15,000 35,000 0.401878 0 8037.551 12056.33 6028.164 14065.72
6 -10,000 15,000 35,000 0.334898 0 -3348.98 0 5023.47 11721.43
7 15,000 35,000 0.279082 0 0 0 4186.225 9767.858
8 3,000,000 15,000 35,000 0.232568 697704.1 0 0 3488.521 8139.881
NPV -302296 -195.688 14718.36 7557.397 25133.93

Ranking by using net present value
Project NPV Ranking
A -302295.88 5
B -195.68759 4
C 14718.364 2
D 7557.397 3
E 25133.926 1
Ranking by using benefit cost ratio
Project BCR Ranking
A 0.697704118 4
B 0.997553905 5
C 1.196244856 2
D 1.151147941 1
E 1.314174081 3
Ranking by using payback period
Project Payback period Ranking
A 8 5
B 4.61 2
C 3.82 1
D 6.03 4
E 5.38 3

11 Calculate the value five year hence of a deposit of US$ 1000 made today if the interest rate is
(i) 8%, (ii) 10%, (iii) 12%, and (iv) 15%
Solution
N=5 , Present value= 1000
(i) When r = 8%
FV=PV (1+i) ^n
FV= 1000(1+ 0.08) ^5 = 1469.33
(ii) When r=10%
FV=PV (1+i) ^n
FV=1000(1+0.1 ) ^5 =1610.51
(iii) When r=12%
FV=PV (1+i) ^n
FV=1000(1+0.12 ) ^5 =1762.34
(iv) When r =15%
FV=PV (1+i ) ^n
FV=1000(1+0.15 ) ^5 =2011.6
12. If you deposit $5000 today at 12% interest rate, in how many years (roughly) will the amount
grow to 60,000?
Solution
Present value =5000/= , Interest rate= 12%, Future value=60,000
PV = FV/ (1+i) ^n
5000 =

=

=

N=21.9 ≈ 22 years

13 At the time of retirement Mr X is given a choice between two alternatives (i) an annual pension of
$ 10000 as long as he lives, and (ii) a lump sum amount of $ 50,000. If this X expects to live for 15 years
and interest rate is 15%, which option to be more attractive
Solution
(i) an ann ual pension of $ 10 000 as long as he lives
n = 15 years , interest rate is 15%,

PVA=A

PVA=10000

PVA=58473.7

Therefore I will advise Mr. X to opt for an annual pensio n of $ 10000 as long as he lives because is more
worthier it bring the total of $ 58473.7 after 15years rather than a lump sum amount of $ 50,000
15. A farmer borrows $25,000 to buy some additional land. He plans to repay the loan over a 10 -year
period with 14% interest. (a) How much additional income would the farmer need each year to amortize
the loan, (b) How much additional income would he need each year to amortize a 20 – year loan. What is
the difference
Solution
CR =PL

Where Pl=principal, i=interest rate, n =number of years
For the ten year
Year unpaid
principal Interest paid
principal Total
1 25000 3500 1292.828 4792.828

2 23707.172 3319.00408 1473.82392 4792.828
3 22233.34808 3112.668731 1680.159269 4792.828
4 20553.18881 2877.446434 1915.381566 4792.828
5 18637.80724 2609.293014 2183.534986 4792.828
6 16454.27226 2303.598116 2489.229884 4792.828
7 13965.04238 1955.105933 2837.722067 4792.828
8 11127.32031 1557.824843 3235.003157 4792.828
9 7892.317151 1104.924401 3687.903599 3774.65
10 4204.413552 588.6178973 4204.210103 4792.828
The farmer need additional income each year to amortize the loan 4792.828/= for ten years
For the 20 years
YEAR Unpaid
principal Interest Paid
principal Total
1 25000 3500 274.65 3774.65
2 24725.35 3461.549 313.101 3774.65
3 24412.249 3417.71486 356.93514 3774.65
4 24055.31386 3367.74394 406.9060596 3774.65
5 23648.4078 3310.777092 463.8729079 3774.65
6 23184.53489 3245.834885 528.8151151 3774.65
7 22655.71978 3171.800769 602.8492312 3774.65
8 22052.87055 3087.401876 687.2481235 3774.65
9 21365.62242 2991.187139 783.4628608 3774.65
10 20582.15956 2881.502339 893.1476613 3774.65
11 19689.0119 2756.461666 1018.188334 3774.65
12 18670.82357 2613.915299 1160.734701 3774.65
13 17510.08887 2451.412441 1323.237559 3774.65
14 16186.85131 2266.159183 1508.490817 3774.65
15 14678.36049 2054.970469 1719.679531 3774.65
16 12958.68096 1814.215334 1960.434666 3774.65
17 10998.24629 1539.754481 2234.895519 3774.65
18 8763.350774 1226.869108 2547.780892 3774.65
19 6215.569882 870.1797835 2904.470216 3774.65
20 3311.099666 463.5539532 3311.096047 3774.65
TOTAL 360664.3116 50493.00362 24999.99638 75493
The farmer need 3774.65 additional income would need each year to amortize a 20 – year loan.

The difference 4792.828 -3774.65 = 1018.178

16. You borrow $7500 to be repaid in 10 equal semiannual payments with 12% interest. What
size of payment must you make annually?
Solution

Unpaid principal, n =5 rate=12%
YEAR Unpaid
principal Interest Paid
principal Total
1 7500 900 1180.573 2080.573
2 6319.427 758.3312 1322.24176 2080.573
3 4997.18524 599.6622 1480.910771 2080.573
4 3516.274469 421.9529 1658.620064 2080.573
5 1857.654405 222.9185 1857.654471 2080.573
TOTAL 24190.54111 2902.865 7500.000066 10402.865

The size of payment you required to make annually is 2080.573 17
17. What is the PV of $ 10,000 you will receive five years fro m today if the discount rate is 10 %?
Solution
PV=10,000, N =5 years , Rate is 10%?
FV=PV (1+i) ^n
FV=10000(1+0.10 ) ^5=16105.1
18. You are offered $ 800 for woodlot. Your estimate is that the timber will worth about 1,400 in
another three years. With a discount rate of 8%, and timber harvesting cost in year three is $ 300,
would you take the offer.
Solution
Present value is 800 Future value is $1400, discount rate of 8% , n=3
Harvesting cost in year three is $ 300

Net worth (FV ) =$14000 -$300=$1100

PV=FV / (1+i) ^n =1100 / (1+0.08 ) ^3
Present value = $873.215
Yes I will take the offer

QUESTION 19
Year Programme A Programme B Discnt factor Discount. Program A Discount. Program B
0 -200,000 -200,000 1 -200000 -200000
1 70,000 70,000 0.892857143 62500 62500
2 70,000 60,000 0.797193878 55803.57143 47831.63265

3 70,000 60,000 0.711780248 49824.61735 42706.81487
4 70,000 60,000 0.635518078 44486.26549 38131.0847
5 70,000 60,000 0.567426856 39719.8799 34045.61134
6 10,000 80,000 0.506631121 5066.311212 40530.48969
NPV 57400.64538 65745.63326
NPV for programme A is 57400.64538
NPV for programme B is 65745.63326
Therefore programme B is most Viable to invest because it has greater Net present value than
program me A
Ranking by using payback period
Programme Payback
period Ranking
A 2.86 1
B 3.2 2
20. The farmers specialized in pig farming has two options (i) or (ii)
i. To sale the recently born 12 piglets each at 25,000 Tshs now OR
ii. To fatten the piglets and sell after 12 months each 50,000 Tshs . (Assuming
fattening cost 30,000; other costs 5,000 per fattener. Also during the period each
piglet will produce 100 kg of manure to be sold at Tshs 50 per kg to nearby farmer).
Assist him to make right decision if interest rate is 25%

SOLUTION
Interest rate is 25%
1st option
12pigilet x25000/=300, 000/=
FV=PV (1+i) ^n
FV=300000(1+0.25 ) ^1=375000

2nd option .fatten piglets

Price=50000 per fatten
Fattening cost 30,000
Other costs = 5,000 per fattener
Each fattener produces 100kg of manure x 12×50 =60,000
Revenue from manure=60,000
Total revenue ( TR) =Price x12+Revenue from manure
(50000 x 12)+60,000
Total revenue= 600000+60000=660000
Total cost=Fattening cost ( all) +other cost for all

TC=30000+5000 x12
TC=30000+60000
TC=90,000
PROFIT= total revenue minus total cost
=660000 -90000
PROFIT=570000
Comments I will assist to go for the second option because the second option has greater profit
than the first option.

21. Suppose someone offers you the following financial contract. If you deposit 10000 US$ with
him, he promise to pay you 2800 annually for 6 years. Using 15% interest rate will you accept
this proposal? Why?
Solution
Deposit 1000 Us$
15% interest rate
Payment 2800 annually
N =6years
Future value for equal payment 2800×6= 16800US$
BUT
While the future value of 10000 for 6 years is
FV=PV (1+0.15 ) ^6 =23130.61$
I will not accept the proposal because future value of 10000$ after six years will be 2330.61$
while annual payment of 2800$ for six years will be only 16800$

22. Calculate the value five year hence of a deposit of US$ 15000 made today if the interest rate
is (i) 6%, (ii) 12%, (iii) 16%, and (iv) 20%
Solution
Deposit of US$ 15000 made today
Interest rate is (i) 6%, (ii) 12%, (iii) 16%, and (iv) 20%
When r=6%
FV=PV (1+i ) ^n
FV=15000(1.06 ) ^5=20073.38
When r= 12%
FV=15000(1.12 ) ^5=26435.13
When r =16%
FV=15000(1.16 ) ^5=31505.125

When r =20%
FV=15000(1.2 ) ^5= 37324.8
23. If you deposit $5000 today at 12% interest rate, in how many years (roughly) will the amount grow
to 60,000?

Solution
Present value =5000/=
Interest rate= 12%
Future value=60,000
PV = FV/ (1+i) ^n
5000=

=

=

n= 21.9 ≈ 22 years

24 Solution
(i) an annual pension of $ 17000 as long as he lives
N= 15 years and interest rate is 12%

PVA=17000

PVA=17000

PVA=115784.69
An annual pension of $ 17 ,000 as long as he lives is more attractive I will advise Mr. X to choose an annual
pension of $17000 because it bring the total of $115784.69 in year 15 than a lump sum amount of $
50,000 .

6 G, 35
B, 21 E, 7
A, 7
C, 25 K, 30

H, 7 J, 1
D, 4 M, 3

F, 1
L, 7

I, 18

key
Critical path
LL
EET=earliest event time
LET=Latest event time

107107
32 32
0 0
1167
7474
104104
3939
77
2929
1273
EL