Question

# If you learn a foreign language, you can improve your compensation at work. Given you are...

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?

1. NPV = PV of all cash flows

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

= -5000/1.060 + 3000/1.060 + 3000/1.061 + 3000/1.062 + 3000/1.063 - 2000/1.063

= -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%

FVPositive Cash Flows = 3000(1.06)3 + 3000(1.06)2 + 3000(1.06)1 + 3000(1.06)0 = 13123.85

FVNegative Cash Flows = 5000(1.06)3 + 2000(1.06)0 = 7955.08

MIRR = (FVPositive Cash Flows/FVNegative Cash Flows)1/n - 1

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

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