Question

The Terug Corporation has been presented with an investment opportunity which will yield end-of-year cash flows of $30,000 per year in Years 1 through 4, $35,000 per year in Years 5 through 9, and $40,000 in Year 10. This investment will cost the firm $150,000 today, and the firm's cost of capital is 10 percent. What are the NPV, IRR and MIRR values for this investment?
a.
NPV $135,984; IRR 17.07%; MIRR 11.27%
b.
NPV $18,023; IRR 16.24%: MIRR 13.27%
c.
NPV $51,138; IRR 16.24%; MIRR 11.27%
d.
NPV $51,138; IRR 17.07%; MIRR 13.27%

Please show work on how you got the answer thank you.

Answer 1

The correct answer is

d.
NPV $51,138; IRR 17.07%; MIRR 13.27%

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Notes:

NPV = Present Value of Cash Inflows - Present Value of Cash Outflows

= [ 30,000 * 1/(1.10)^ 1 + 30,000 * 1/(1.10)^ 2 +30,000 * 1/(1.10)^ 3 +30,000 * 1/(1.10)^ 4 + 35,000 * 1/(1.10) ^ 5 +35,000 * 1/(1.10) ^6 +35,000 * 1/(1.10) ^7+35,000 * 1/(1.10) ^8+35,000 * 1/(1.10) ^9 + 40,000 * 1/(1.10) ^ 10 ] - $ 150,000

= $ 201,138.24- $ 150,000

= $ 51,138.24

= $ 51,138

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Let the IRR be x.

Now , Present Value of Cash Outflows=Present Value of Cash Inflows

150,000= 30,000/(1.0x) + 30,000/ (1.0x)^2 + 30,000/ (1.0x)^3+30,000/ (1.0x)^4 + 35,000/ (1.0x)^5 + 35,000/ (1.0x)^6+35,000/ (1.0x)^7+35,000/ (1.0x)^8+35,000/ (1.0x)^9 +40,000/ (1.0x)^10

Or x = 17.065%

= 17.07%

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Future Value = Present Value of Cash Inflows * ( 1+Rate /100) ^ Time

= $ 201,138.24 * ( 1+10/100) ^ 10

= $ 521,700.7934

Hence, MIRR=[Future value of inflows/Present value of outflow]^(1/n)-1

=[$ 521,700.7934/ 150,000] ^ (1/10)-1

= 13.27472691%

= 13.27%