Question

Figure 14-11.

Present value of an Annuity of $1 in Arrears

Periods	4%	6%	8%	10%	12%	14%
1	0.962	0.943	0.926	0.909	0.893	0.877
2	1.886	1.833	1.783	1.736	1.690	1.647
3	2.775	2.673	2.577	2.487	2.402	2.322
4	3.630	3.465	3.312	3.170	3.037	2.914
5	4.452	4.212	3.993	3.791	3.605	4.433
6	5.242	4.917	4.623	4.355	4.111	3.889
7	6.002	5.582	5.206	4.868	4.564	4.288
8	6.733	6.210	5.747	5.335	4.968	4.639
9	7.435	6.802	6.247	5.759	5.328	4.946
10	8.111	7.360	6.710	6.145	5.650	5.216

Problem 14-15

Refer to Figure 14-11. Cleves Company is considering two projects.

	Project X		Project Y
Initial investment	$500,000		$100,000
Annual cash flows	$88,500		$34,320
Life of the project	10 years		4 years
Depreciation per year	$50,000		$25,000

Cleves requires a minimum rate of return of 8 percent.

Required:

A. What is the accounting rate of return for each project? If required, round your answers to two decimal places.

Project X, ARR	%
Project Y, ARR	%

B. What is the net present value for each project?

Project X, NPV	$
Project Y, NPV	$

C. What is the internal rate of return for each project?

Project X, IRR	%
Project Y, IRR	%

D. Given that only one project can be selected, which project should be chosen?

Answer 1

A. ARR means Average Rate of Return or Accounting Rate of Return.

It is a measure to derive the Rate of Return but it doesn’t consider the Time Value of Money, It is measured by dividing the Average Annual Profit by the Initial Investment. Average Annual Profit can be derived in this case by deducting the depreciation from the annual cash flows.

Project X:

Average annual profit = $38,500 ($88,500 - $50,000)

Initial investment = $500,000

ARR = 7.7%

Project Y:

Average annual profit = $9,320 ($34,320 - $25,000)

Initial investment = $100,000

ARR = 9.32%

Cleves minimum rate of return is 8%, if ARR is the measure to chose, Project-X would be rejected by accepting Project-Y.

B. NPV

NPV refers to the Net Present Value, the measure by which we can decide whether to invest in the project or not. If the NPV is greater than 0, it is profitable to invest, otherwise it is not recommended. NPV is calculated by deducting the discounted cash outflows from the discounted cash inflows and discounting factor used is the Cost of Capital of the Project. In this case we can take the discounting factor as 8% as it is the minimum expected return.

NPV is calculated as follows:

Project-X:

Project-Y:

From the above table it is evident that NPV is positive with a value of $93,835 for Project X and $13,667.84 for Project Y, hence it is acceptable to invest in the proposed projects.

C. IRR

IRR refers to the Internal Rate of Return, it is the rate at which the NPV of the project equals to 0. It is the highest rate of return which can be achieved from the proposed investment.

Generally, it is easy to compute IRR by taking the discounting values at two different discount factors and deriving thereupon.

IRR is calculated as follows:

Project X:

Since, NPV at 12% is $ 25 and at 14% is $ (38,384) , we can find the rate at which NPV will be 0 as follows,

= [14%] – [(38,384 - 25) ÷ 38,384] × 2%

= 14 - 1.9987

= 12.0013%

Project Y:

Since, NPV at 14% is $ 8.48 and at 16% is $ (3,972.64) , we can find the rate at which NPV will be 0 as follows,

= [16%] – [(3,972.64 – 8.48) ÷ 3,972.64] × 2%

= 16 - 1.9957

= 14.0043%

When IRR is concerned, Project - Y is beneficial than Project - X but both are feasible as the IRR is more than the minimum expected return.

D. If only one project can be selected, then this becomes the case of mutually exclusive projects. In this case, NPV favours Project X and IRR favors Project Y as the respective projects hold good in those measures. In this conflict, we always consider the project with higher NPV as it theoritically sounds good. In such a situation, one should go with Project X.