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 $3,000 more per year for the next 3 years starting a year from today before you move onto a new job. 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. The NPV is calculated by adding the present value for all the years. The formula for present value is

PV = CFn / (1+IRR)^n

Here n = the period and CF is the cash flow and IRR is the rate of return.

We calculate the PV for each of the period and the answer is 1339.80

The NPV for learning new language is 1339.80

2. In order to calculate the IRR we need to make sure that the NPV =0. This is done by using the formula

NPV = 0 = Summation (CFn / (1+IRR)^n)

This means we kind of have to work backword into the NPV. However, using excel we usually take help from the solver to solve this problem. Set up the solver parameters as shown below and then find the solution.

The answer is the IRR = 22%

2. In order to identify the MIRR, we use a formula

MIRR = nth root (FV/PV) – 1

FV is the future value positive cash flows at cost of capital

PV is the initial expense at cost of capital

Other way is to use an excel formula to do it quicker. It is shown below and the answer is

15%