Question

If you learn a foreign language, you can improve your compensation at work. Given you are not good at learning languages, you estimate today you would need to spend $5,000 to learn a language. You then believe you can earn an extra $3,000 per year for 4 years starting *today* before you move onto a new job. (The last $3,000 occurs three years from today.) However, you will also pay back $2,000 to the company exactly 3 years from today since some of your clients will leave with you. Your discount rate is 6% APR.

1. What is the NPV of learning a new language?

2. What is the IRR?

3. What is the MIRR if you use the discount rate as the reinvestment rate?

Answer #1

1. NPV = PV of all cash flows

NPV = Σ CF^{n}/(1+r)^{n} , where CF is the cash
flow in period n and r is the APR

= -5000/1.06^{0} + 3000/1.06^{0} +
3000/1.06^{1} + 3000/1.06^{2} +
3000/1.06^{3} - 2000/1.06^{3}

= -5000 + 3000 + 2830.19 + 2669.99 + 2518.86 - 1679.24 = $4,339.9

2. IRR is the rate of return when NPV = 0

Let IRR = i

=> -5000/(1+i)^{0} + 3000/(1+i)^{0} +
3000/(1+i)^{1} + 3000/(1+i)^{2} +
3000/(1+i)^{3} - 2000/(1+i)^{3} = 0

Solve for i to get i = 126.117%

3. Reinvestment Rate = financing rate = 6%

FV_{Positive Cash Flows} = 3000(1.06)^{3} +
3000(1.06)^{2} + 3000(1.06)1 + 3000(1.06)^{0} =
13123.85

FV_{Negative Cash Flows} = 5000(1.06)^{3} +
2000(1.06)^{0} = 7955.08

MIRR = (FV_{Positive Cash Flows}/FV_{Negative Cash
Flows})^{1/n} - 1

= (13123.85/7955.08)^{1/3} - 1 = 1.1816 - 1 = 0.1816 =
18.16%

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