Question

You are contemplating the purchase of a new $1,840,000 computer-based dairy cow
feeding system. The system will be depreciated straight-line over its ten-year life and
have no value at the end of its life. You will earn $250,000 before taxes in the first year
from additional milk production and expect an annual growth rate of 4%. Your tax rate is
25%, equity cost 10%, and debt cost 7%. Currently, your farm’s debt to asset ratio is 0.25
and you would like to keep the same financial ratio.

a. Compute the following for this project using after-tax cash flows: (1) payback period,
(2) NPV, and (3) internal rate of return. Please also list cash flows for each year.

b. Based on the NPV and IRR methods, should you make the purchase?
c. Explain what assumptions are for NPV and IRR methods.

Answer 1

Answer :

Pay back period : It is the amount of time required to recover the original cost of the project

Payback period = 7.13 years

Year	Cash flow		Payback period
0	-18,40,000	-1840000	1
1	2,33,500	-1606500.00	1
2	2,41,000	-1365500.00	1
3	2,48,800	-1116700.00	1
4	2,56,912	-859788.00	1
5	2,65,348	-594439.52	1
6	2,74,122	-320317.10	1
7	2,83,247	-37069.78	0.1266316
8	2,92,737	255667.42	-
9	3,02,607	558274.12	-
10	3,12,871	871145.09	-
			7.1266316

Tax Rate 25%

(a). Initial cash outlay = Purchase cost + training cost + installatiion cost+increase in working capital

18,40,000

1840000

0

0

0

(b). Cash flow for the year = [(revenue-cost)*(1-tax rate)] + tax shield due to depreciation

-18,40,0000	0	-	-	-	-
2,33,500	1	250000	0	75%	184000
2,41,000	2	260000	0	75%	184000
2,48,800	3	270400	0	75%	184000
2,56,912	4	281216	0	75%	184000
2,65,348	5	292464.6	0	75%	184000
2,74,122	6	304163.2	0	75%	184000
2,83,247	7	316329.8	0	75%	184000
2,92,737	8	328982.9	0	75%	184000
3,02,607	9	342142.3	0	75%	184000
3,12,871	10	355828.0	0	75%	184000

(c). Net present value = present value of cash inflow-initial cash outlay

Discounted at required rate of return of 9.05%(0.8*10)+(0.2*7*0.75)

NPV -1,43,494

IRR 7.33%

NPV = Present value of cash inflow- the present value of cash outflow

IRR : It is the discount rate at which present value of projects cash outflows (cost) is equal to the present value of projects cash inflow.