Question

Joetz Corporation has gathered the following data on a proposed investment project (Ignore income taxes.):

Investment required in equipment	$	33,500
Annual cash inflows	$	7,400
Salvage value of equipment	$	0
Life of the investment		15	years
Required rate of return		10	%

The company uses straight-line depreciation on all equipment. Assume cash flows occur uniformly throughout a year except for the initial investment.

Click here to view Exhibit 13B-1 and Exhibit 13B-2, to determine the appropriate discount factor(s) using the tables provided.

The internal rate of return of the investment is closest to:

Multiple Choice

• 23%

• 21%

• 19%

• 25%

Answer 1

Internal rate of return is the the rate at which net present value is zero. Therefore internal rate of return would be the discounting rate at which present value of cash inflows is equal to initial investment.

Calculation of Internal Rate of Return :-

Let the two rate for the range of internal rate of return is 20% and 23%.

Net Present Value at 20% = PV of Cash Inflows - Initial Investment

= [Cash Inlfows*PVAF(20%, 15 yrs)] - $33,500

= ($7,400*4.6754726) - $33,500

= $34,598 - $33,500 = $1,098

Net present Value at 23% = PV of Cash Inflows - Initial Investment

= [Cash Inlfows*PVAF(23%, 15 yrs)] - $33,500

= ($7,400*4.1529783) - $33,500

= $30,732 - $33,500 = -$2,768

IRR = r1+{[NPV1/(NPV1 - NPV2)]*(r2-r1)}

(Where,

r1 = Lower discount rate

r2 = Higher discount rate

NPV1 = NPV at lower discount rate

NPV2 = NPV at higher discount rate)

IRR = 20%+{[1,098/(1,098+2,768)]*(23%-20%)}

= 0.20+[(1,098/3,866)*3%]

= 0.20+0.0085 = 0.2085 or 20.85%

Therefore internal rate of return of the investment is 20.85% (approximately) which is closest to 21%.

Hence the correct option is B) 21%.