Question

Consider the following two alternatives that have no salvage value:

	A	B
Initial Cost	$15,000	$5,100
Uniform Annual Benefits	$3,000	$1,800
Useful life, in years	8	4

a) If the MARR is 10%, which alternative is preferred?

b) Determine the ranges of MARR rate within which 1) A is preferred; 2) B is preferred and 3) Neither alternative should be chosen. Justify your answer through rate of return and incremental analysis.

Answer 1

Calculating the annual worth of the two alternatives.

Calculating the AW of alternative A.

Now calculation the AW of alternative B.

At a rate of 10% alternative B will be preferred.

B. Refer the calculation done using excel function

Calculating the IRR of alternative A manually

The net present worth of alternative A can be written as

Assume rate = 11%

Now assuming rate = 12%

Now, applying linear interpolation we get

Similarly, we can calculate the IRR of alternative B. The NPW of the alternative B can be expressed as (Note for 4 years as well as 8 years the IRR would remain same).

Assume rate = 15%

Now, assume rate = 16%

Now applying linear interpolation

Similarly we can determine the incremental IRR using the manual method. The NPW can be expressed as

Assume the rate = 10%

Now assume rate = 9%

Now applying linear interpolation we get

When MARR is equal to 10% then alternative B will be preferred.

When MARR = 9%, then alternative A will be preferred.

Alternative A will be preferred when MARR is less than 11.81%.

Alternative B will be preferred when MARR is less than 15.38%.

When the MARR is greater 15.38% then no alternative will be selected.

In terms of incremental IRR when MARR is less than 9.96% then A will be preferred. When MARR is greater than equal to 9.96% then alternative B will be selected.

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