Kevin has $100,000 and is considering the following two investment opportunities

Question

Kevin has $100,000 and is considering the following two investment opportunities. Investment A requires an initial investment of $100,000 and promises to return an annual amount of $23,740 for 5 years. Investment B requires an initial investment of $90,000 and is expected to return $21,150 every year for 5 years. If the Kevin’s MARR is 5% per year compounded annually, which investment should Kevin choose, if any. Solve using the internal rate of return approach. (Note: You must solve for IRR rounded to the nearest whole %.)

(Please Do Not Use Excel!!!)

Explanation / Answer

IRR = RL + [NPVL / (NPVL - NPVH)] x (RH - RL) where

RH: Higher interest rate = 12% (assumed),

RL: Lower interest rate = 6% (assumed)

NPVH: NPV at higher rate

NPVL: NPV at lower rate

For Investment A,

IRR = 6% + [2 / (2 + 14,423)] x (12 - 6)%

= 6% + (2 / 14,425) x 6%

= 6% + 0 x 6%

= 12%

For investment B,

IRR = 6% + [- 909 / (- 909 + 13,759)] x (12 - 6)%

= 6% + (- 909 / 12,841) x 6%

= 6% - 0.07 x 6%

= 6% - 0.42%

= 5.58%

~ 6%

Though both investments have IRR higher than MARR, since Investmen A has a higher IRR, A has to be chosen.

INVESTMENT - A Year Cash Flow Discount factor@6% Discounted Cash Flow: @6% Discount factor@12% Discounted Cash Flow: @12% (A) (B) (A) x (B) (D) (A) x (D) 0 -1,00,000 1.0000 -1,00,000 1.0000 -1,00,000 1 23,740 0.9434 22,396 0.8929 21,196 2 23,740 0.8900 21,129 0.7972 18,925 3 23,740 0.8396 19,933 0.7118 16,898 4 23,740 0.7921 18,804 0.6355 15,087 5 23,740 0.7473 17,740 0.5674 13,471 NPV = 2 NPV = -14,423 INVESTMENT - B Year Cash Flow Discount factor@6% Discounted Cash Flow: @6% Discount factor@12% Discounted Cash Flow: @12% (A) (B) (A) x (B) (D) (A) x (D) 0 -90,000 1.0000 -90,000 1.0000 -90,000 1 21,150 0.9434 19,953 0.8929 18,884 2 21,150 0.8900 18,823 0.7972 16,861 3 21,150 0.8396 17,758 0.7118 15,054 4 21,150 0.7921 16,753 0.6355 13,441 5 21,150 0.7473 15,805 0.5674 12,001 NPV = -909 NPV = -13,759

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