Exercise 24-7 Iggy Company is considering three capital expenditure projects. Re
ID: 2588549 • Letter: E
Question
Exercise 24-7 Iggy Company is considering three capital expenditure projects. Relevant data for the projects are as follows. Annual Life of Project Investment Income Project $241,900 $17,540 6 years 273,300 20,750 9 years 15,700 7 years 22A 23A 24A 282,400 Annual income is constant over the life of the project. Each project is expected to have zero salvage value at the end of the project. Iggy Company uses the straight-line method of depreciation. her Determine the internal rate of return for each project. (Round answers O decimal places, e.g. 10. For calculation purposes, use 5 decimal places as displayed in the factor table provided.) Internal Rate Project Return 22A 23A 24AExplanation / Answer
Answer
22A
23A
24A
Initial cash Outflow
241,900
273,300
282,400
Annual Cash Inflow
17,540
20,750
15,700
Useful Life
6 Years
9 Years
7 Years
Depreciation
40,316.67
30,366.67
40,342.86
Cash Inflow after Depreciation
57,856.67
51,116.67
56,042.86
Depreciation = Investment / No. of years
Cash Inflow after depreciation = Net income + Depreciation
For calculation of Net cash inflow we will add back depreciation amount as depreciation is a NON Cash expense.
IRR is rate which satisfies the following condition:
Present Value of Cash inflows = Initial Cash outflow
Cash Inflow per year * PVAF of required project = Initial Cash Outflow
22A
57,856.67 * PVAF = 241,900
PVAF = 4.181
23A
51,116.67* PVAF = 273,300
PVAF = 5.346
24A
56,042.86 * PVAF = 282,400
PVAF = 5.039
Now we will to find which Rate of capital has these PVAF at required years.
22A = PVAF of 4.181 is between 11% and 12%
23A = PVAF of 5.346 is between 11% and 12%
24A = PVAF of 5.039 is between 8% and 9%
IRR = Lower rate + NPV (L) / [NPV (L) – NPV (H)] * (H-L) Rate
22A
PVAF @11% for 6 Years = 4.231
PVAF @12% for 6 Years = 4.111
NPV@11% for 6 Years = (57,856.67 * 4.231) - 241,900 = 2,891.57
NPV@12% for 6 Years = (57,856.67 * 4.111) - 241,900 = (4,051.23)
IRR = 11% + [2,891.57 / (2,891.57 – (-4,051.23))] * (12-11)
=11% + [2,891.57 / (2,891.57 + 4,051.23)] * (12-11)
= 11% + (2,891.57 / 6942.8)*1%
IRR of 22A= 11.416%
23A
PVAF @11% for 9 Years = 5.537
PVAF @12% for 9 Years = 5.328
NPV@11% for 9 Years = (51,116.67* 5.537) - 273,300= 9,733
NPV@12% for 9 Years = (51,116.67* 5.328) - 273,300= (950.38)
IRR = 11% + [9,733/ (9,733+ 950.38)] * (12-11)
= 11% + (9,733/ 10,683.38)*1%
IRR of 23A= 11.911%
24A
PVAF @8% for 7 Years = 5.206
PVAF @9% for 7 Years = 5.032
NPV@11% for 9 Years = (56,042.86 * 5.206) - 282,400= 9,359.13
NPV@12% for 9 Years = (56,042.86 * 5.032) - 282,400 = (392.33)
IRR = 8% + [9,359.13/ (9,359.13+ 392.33)] * (9-8)
= 8% + (9,359.13/ 9,751.46)*1%
IRR of 24A= 8.96%
It is recommended to choose Project 22A as IRR is lower is that case.
22A
23A
24A
Initial cash Outflow
241,900
273,300
282,400
Annual Cash Inflow
17,540
20,750
15,700
Useful Life
6 Years
9 Years
7 Years
Depreciation
40,316.67
30,366.67
40,342.86
Cash Inflow after Depreciation
57,856.67
51,116.67
56,042.86
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