Chapter 3
Capital Budgeting
Decision
NUMERICAL PROBLEMS
Problem 1
Project Namaste has a cost a 50,000, and its expected net cash inflows are Rs. 10,000 per
year for 8 years.
a. What is the project payback period (to the closest year)?
b. Should project kathmandu accepted? if the maximum cost recovery time is 4 years.
c. The required rate of return or the project is 10 percent. What is the project's NPV?
Interpret.
d. What is the project's IRR? Interpret.
e. What is the project's discounted payback period, assuming a 12 percent required rate
of return? Interpret.
f. What is the project's profitability index? Interpret.
Ans: a) 5 years, b) This project is rejected, c) Rs. 3349, d) 16%, e) No f) 1.067
Solution
Given,
Initial investment = Rs. 50,000
Expected net cash inflows per year for 8 years = Rs. 10,000
Life of projects (n) = 8 years
a. Calculation of project’s payback period
Here, Cash inflows are even
We have,
Initial Investment Rs. 50000
Payback period = Annual Cash Inflow = Rs. 10000 = 5 years
b. Actual payback period > maximum recover payback period = 4 years This project
should not be accepted.
c. Calculation of NPV, when the cost of capital for the project is 10%
For even cash inflows,
NPV = Total present value of cash inflows – PV of initial investment.
Total present value of cash inflows = Annual cash inflows [PVIFAk,n]
,26 Basic Financial Management
∴ Total PV of cash inflows = Rs. 10,000 [PVIFA10%,8]
= 10,0000 × 5.3349 = 5.3349
NPV = 53349 – 50,000 = 3349
The project’s NPV is Rs. 3349. Since project’s NPV is positive, therefore project should
be accepted.
d. Calculation of Project’s IRR
Step i:
Initial Investment Rs. 50000
Factor = Annual Cash Inflow = Rs. 10000 = 5.0000
Step ii:
The factor 5.000 lies between 11% & 12%.
Step iii: Using the trial & error Approach
∴ NPVLR = CFAT × PVIFA11% 8 y – NCO
= 10,000 × 5.1461 – 50,000
= Rs. 1461 (∴ +ve always)
Try at i = 12%
NPVHR = CFAT × PVIFA 12% 8y – NCO
= 10,000 × 4.9676 – 50,000
= - Rs. 324 ( ∴ -ve always)
Step iv : By Interpolation
NPVLR
Actual IRR = LR + NPV – NPV (HR – LR)
LR HR
1461
= 11% + 1461 – (-324) (12% – 11%)
= 11.82%
Decision Rule:
If Actual IRR = 11.82% > i or WACC = 10% > i or WACC = 10% This Project should
be Accepted.
The factor 4.3438 lies nearly at 16% for 8 years, according to present value of annuity
table.
e. Calculation of Project’s Discounted Payback Period
Cost of capital = 12%
We have,
Discounted payback period
Amt. to be recover
= minimum year + PV of next year cash flow
, Chapter 2| Cost of Capital 27
Year Cash flow PVIF@12% PV of cash flow Cumulative PV of cash flow
0 (50,000) 1 (50,000) (50,000)
1 10,000 0.8929 8929 (41071)
2 10,000 0.7972 7972 (33099)
3 10,000 0.7118 7118 (25981)
4 10,000 0.6255 6255 (197296)
5 10,000 0.5674 5674 (14052)
6 10,000 0.5066 5066 (8986)
7 10,000 0.4523 4523 (4463)
8 10,000 0.4039 4039 (424)
Now,
Discounted payback period
Amt. to be recover
= minimum year + PV of next year cash flow
2788
= 6 + 5428 = 6.51 year
(∴ DPBP = Above 8 yrs P.V. of cash in flows is not recover during the project life so
cannot calculated)
TPV Rs. 53349
f. Profitability index (PI) = NCO = Rs. 50000 = 1.067 (∴ P.I. = 1.067 > 1 This project
should e Accepted.
Problem No. 2
Gaurishankar engineering is considering including two pieces of equipment a truck and an
overhead pulley system in this year's capital budget. The projects are independent. The
cash outlay for the truck is Rs.1 7,100 and that for the pulley system is Rs. 22,430. Each
piece of equipment has an estimated life of 5 years. The annual after-tax cash flow expect to
be provide by the truck is Rs. 5,100 and for the pulley, it is Rs. 7,500. The firm's required
rate of return is 14 percent. Calculate the IRR, the NPV, and the payback period for each
project, and indicate which projects should be accepted.
Ans: NPVT = 408.8, NPVPT = 3318.25, IRR T = 15%, IRRp = 20%
Solution:
Given,
Truck Pulley System
Net cash outlay (NCO) Rs. 17100 Rs. 22430
Annual net cash in flow Rs. 5100 Rs. 7500
Expected life 5 years 5 years
Required rate of return 14% 14%
NPV ? ?
IRR ? ?
a) Calculation of NPV for each project
NPV for Truck system
Year Cash flow (CF) D.F. @ 14% PV of Cash flow
0 (Rs. 17100) 1 (Rs. 17,100)
1 to 5 Rs. 5,100 3.4331 Rs. 17,508.8
, 28 Basic Financial Management
NPV = Rs. 408.8
Therefore, NPV for truck is Rs. 408.8
NPV for pulley system
Year Cash flow (CF) D.F. @ 14% PV of Cash flow
0 (Rs. 22,430) 1 (Rs. 22,430)
1 to 5 Rs. 7500 3.4331 Rs. 25,748.25
NPV = Rs. 3318.25
Therefore, NPV for pulley system is RRs. 3318.25
b) Calculation of IRR for each project
Net cash outlay
Factor = Annula cash in flow
Rs. 17100
Factor = . Rs. 5100 = 3.3529
According to the PVIFA table the value of 3.3529 lies in 15% so IRR is 15% if can be
provided as folllows:
Now,
NPV of cash inflow at 15% = CFAT (PVIFAk, n years) – NCO
= Rs. 5100 ((PVIFA15%, 5 years) – Rs. 17,100
= Rs. 5100 (3.3522) – Rs. 17,100
= –Rs. 3.78
[Vary due to decimal calculation]
IRR for pulley system
Net cash outlay Rs. 22430
Factor = Annual cash in flow = Rs. 7500 = 2.9906
According to the PVIFA table the factor value of 2.9906 lies in exactly at 20% .
Therefore, IRR is 20%
Decision:
If they are in dependent project. Both projects should be accepted because both
projects have positive NPVs and IRR is higher than cost of capital.
Problem No. 3
The following are exercise on internal rate of return:
a) An investment of rs. 1,000 today will return Rs. 2,000 at the end of 10 years. What is its
internal rate of return?
b) An investment of rs. 1,000 will return Rs. 500 at the end of each of the next years.
What is its internal rate of return?
c) An investment of Rs. 1,000 today will return Rs. 900 at the end of 1 year, Rs. 500 at the
end of 2 years and Rs. 100 at the end of 3 years What is its internal rate of return?
d) `An investment of Rs. 1,000 will return Rs. 130 per year forever, what is its internal
rate of return?
Ans: a) 7.18% b) 23.40% c) 34.20% d) 13%
Solution:
a) Net cash flow (NCO) = Rs. 1,000
CFAT of tenth year = Rs. 2,000
Capital Budgeting
Decision
NUMERICAL PROBLEMS
Problem 1
Project Namaste has a cost a 50,000, and its expected net cash inflows are Rs. 10,000 per
year for 8 years.
a. What is the project payback period (to the closest year)?
b. Should project kathmandu accepted? if the maximum cost recovery time is 4 years.
c. The required rate of return or the project is 10 percent. What is the project's NPV?
Interpret.
d. What is the project's IRR? Interpret.
e. What is the project's discounted payback period, assuming a 12 percent required rate
of return? Interpret.
f. What is the project's profitability index? Interpret.
Ans: a) 5 years, b) This project is rejected, c) Rs. 3349, d) 16%, e) No f) 1.067
Solution
Given,
Initial investment = Rs. 50,000
Expected net cash inflows per year for 8 years = Rs. 10,000
Life of projects (n) = 8 years
a. Calculation of project’s payback period
Here, Cash inflows are even
We have,
Initial Investment Rs. 50000
Payback period = Annual Cash Inflow = Rs. 10000 = 5 years
b. Actual payback period > maximum recover payback period = 4 years This project
should not be accepted.
c. Calculation of NPV, when the cost of capital for the project is 10%
For even cash inflows,
NPV = Total present value of cash inflows – PV of initial investment.
Total present value of cash inflows = Annual cash inflows [PVIFAk,n]
,26 Basic Financial Management
∴ Total PV of cash inflows = Rs. 10,000 [PVIFA10%,8]
= 10,0000 × 5.3349 = 5.3349
NPV = 53349 – 50,000 = 3349
The project’s NPV is Rs. 3349. Since project’s NPV is positive, therefore project should
be accepted.
d. Calculation of Project’s IRR
Step i:
Initial Investment Rs. 50000
Factor = Annual Cash Inflow = Rs. 10000 = 5.0000
Step ii:
The factor 5.000 lies between 11% & 12%.
Step iii: Using the trial & error Approach
∴ NPVLR = CFAT × PVIFA11% 8 y – NCO
= 10,000 × 5.1461 – 50,000
= Rs. 1461 (∴ +ve always)
Try at i = 12%
NPVHR = CFAT × PVIFA 12% 8y – NCO
= 10,000 × 4.9676 – 50,000
= - Rs. 324 ( ∴ -ve always)
Step iv : By Interpolation
NPVLR
Actual IRR = LR + NPV – NPV (HR – LR)
LR HR
1461
= 11% + 1461 – (-324) (12% – 11%)
= 11.82%
Decision Rule:
If Actual IRR = 11.82% > i or WACC = 10% > i or WACC = 10% This Project should
be Accepted.
The factor 4.3438 lies nearly at 16% for 8 years, according to present value of annuity
table.
e. Calculation of Project’s Discounted Payback Period
Cost of capital = 12%
We have,
Discounted payback period
Amt. to be recover
= minimum year + PV of next year cash flow
, Chapter 2| Cost of Capital 27
Year Cash flow PVIF@12% PV of cash flow Cumulative PV of cash flow
0 (50,000) 1 (50,000) (50,000)
1 10,000 0.8929 8929 (41071)
2 10,000 0.7972 7972 (33099)
3 10,000 0.7118 7118 (25981)
4 10,000 0.6255 6255 (197296)
5 10,000 0.5674 5674 (14052)
6 10,000 0.5066 5066 (8986)
7 10,000 0.4523 4523 (4463)
8 10,000 0.4039 4039 (424)
Now,
Discounted payback period
Amt. to be recover
= minimum year + PV of next year cash flow
2788
= 6 + 5428 = 6.51 year
(∴ DPBP = Above 8 yrs P.V. of cash in flows is not recover during the project life so
cannot calculated)
TPV Rs. 53349
f. Profitability index (PI) = NCO = Rs. 50000 = 1.067 (∴ P.I. = 1.067 > 1 This project
should e Accepted.
Problem No. 2
Gaurishankar engineering is considering including two pieces of equipment a truck and an
overhead pulley system in this year's capital budget. The projects are independent. The
cash outlay for the truck is Rs.1 7,100 and that for the pulley system is Rs. 22,430. Each
piece of equipment has an estimated life of 5 years. The annual after-tax cash flow expect to
be provide by the truck is Rs. 5,100 and for the pulley, it is Rs. 7,500. The firm's required
rate of return is 14 percent. Calculate the IRR, the NPV, and the payback period for each
project, and indicate which projects should be accepted.
Ans: NPVT = 408.8, NPVPT = 3318.25, IRR T = 15%, IRRp = 20%
Solution:
Given,
Truck Pulley System
Net cash outlay (NCO) Rs. 17100 Rs. 22430
Annual net cash in flow Rs. 5100 Rs. 7500
Expected life 5 years 5 years
Required rate of return 14% 14%
NPV ? ?
IRR ? ?
a) Calculation of NPV for each project
NPV for Truck system
Year Cash flow (CF) D.F. @ 14% PV of Cash flow
0 (Rs. 17100) 1 (Rs. 17,100)
1 to 5 Rs. 5,100 3.4331 Rs. 17,508.8
, 28 Basic Financial Management
NPV = Rs. 408.8
Therefore, NPV for truck is Rs. 408.8
NPV for pulley system
Year Cash flow (CF) D.F. @ 14% PV of Cash flow
0 (Rs. 22,430) 1 (Rs. 22,430)
1 to 5 Rs. 7500 3.4331 Rs. 25,748.25
NPV = Rs. 3318.25
Therefore, NPV for pulley system is RRs. 3318.25
b) Calculation of IRR for each project
Net cash outlay
Factor = Annula cash in flow
Rs. 17100
Factor = . Rs. 5100 = 3.3529
According to the PVIFA table the value of 3.3529 lies in 15% so IRR is 15% if can be
provided as folllows:
Now,
NPV of cash inflow at 15% = CFAT (PVIFAk, n years) – NCO
= Rs. 5100 ((PVIFA15%, 5 years) – Rs. 17,100
= Rs. 5100 (3.3522) – Rs. 17,100
= –Rs. 3.78
[Vary due to decimal calculation]
IRR for pulley system
Net cash outlay Rs. 22430
Factor = Annual cash in flow = Rs. 7500 = 2.9906
According to the PVIFA table the factor value of 2.9906 lies in exactly at 20% .
Therefore, IRR is 20%
Decision:
If they are in dependent project. Both projects should be accepted because both
projects have positive NPVs and IRR is higher than cost of capital.
Problem No. 3
The following are exercise on internal rate of return:
a) An investment of rs. 1,000 today will return Rs. 2,000 at the end of 10 years. What is its
internal rate of return?
b) An investment of rs. 1,000 will return Rs. 500 at the end of each of the next years.
What is its internal rate of return?
c) An investment of Rs. 1,000 today will return Rs. 900 at the end of 1 year, Rs. 500 at the
end of 2 years and Rs. 100 at the end of 3 years What is its internal rate of return?
d) `An investment of Rs. 1,000 will return Rs. 130 per year forever, what is its internal
rate of return?
Ans: a) 7.18% b) 23.40% c) 34.20% d) 13%
Solution:
a) Net cash flow (NCO) = Rs. 1,000
CFAT of tenth year = Rs. 2,000
