Question

Three mutually exclusive design alternatives are being considered. The estimated cash flows for each alternative are given below. The MARR is 12​% per year. At the end of the useful​ life, the investment will be sold. A​ decision-maker can select one of these alternatives or decide to select none of them. Make a recommendation using the PW method.

	X	Y	Z
Investment cost	​$275,000	​$140,000	​$370,000
Annual revenue	​$85,840	​$53,207	​$93,911
Annual cost	​$23,183	​$14,370	​$20,543
Useful life	15 years	15 years	15 years
IRR	21.6​%	27.0​%	18.2​%
PW	​$151,748	​$124,514	​$129,700

​(a) Which alternative is the most​ economical? Choose the correct answer below.

(A) Alternative Z

(B) None of the alternatives

(C) Alternative Y

(D) Alternative X

​(b) Calculate the discounted payback period of each alternative.

The discounted payback period of alternative X is______years. (Round to the nearest​ decimal.)                                          

The discounted payback period of alternative Y is______years.​(Round to the nearest​ decimal.)                                               

The discounted payback period of alternative Z is_____years.​(Round to the nearest​ decimal.)

Based on the payback​ period, which alternative is the most​ preferred? Choose the correct answer below.

(A) Alternative Z

(B) Alternative Y

(C) None of the alternatives

(D) Alternative X

​(c) Why could the answers in​ (a) and​ (b) be​ different?

Answer (A) because the payback period method ignores the cash flows after the payback period

Answer (B)because the payback period gives more weight to the cash flows after the payback period

Answer 1

Calculated the incremental IRR between the three projects. First calculated the Incremental IRR between X and Y (These two projects because Y has the minimum initial investment and X has second lowest investment). The incremental IRR = 15.7% (greater than MARR). Select alternative X over Y.

Now comparing X with Z we get ∆IRR = 7.4%. thus select alternative X.

Select alternative X.

b. Calculating of Discounted payback period.

Calculation for X

Discounted pay back period = 6 + (17,391.55/28,342.8) = 6.6 years

Calculation for Y

DPBP = 5 + (1.31 /19,676) = 5.0 years

Now calculating for Z

DPBP = 8 + (5,534.21/26,457.2) = 8.2 years

C. Based on DPBP select alternative Y.

The discount is the discounted value. That is the present value of the cash flow at T = 0,at a rate of 12%.

Why could the answers in​ (a) and​ (b) be​ different?

Answer (A) because the payback period method ignores the cash flows after the payback period.