Question

1. Carla earns $100,000 per year now, and pays $20,000 per year on her fixed rate mortgage. Her income is subject to a COLA clause. If the risk-free rate of interest is 3%, and the expected inflation rate is 2% per year, what is the spending power of her net income in 10 years, expressed in today’s dollars?

2. How would you find the present value of 10 years of Carla’s income without being given an inflation rate or interest rate? HINT: Use market data to determine your answer.

Answer 1

Answer 1.

Carla's income today = $100,000

Fixed rate mortgage = $20,000

Risk free rate = 3%

Inflation rate = 2%

Carla's income will increase with inflation. So, 10 years from now, she will earn:

Future Value = Present Value x (1+r)^n

FV = 100,000 x (1+0.02) ^ 10

Therefore, FV = $ 121,899.44

She will earn annual salary $121,899.44

Out of that, she will pay $20,000 mortgage.

Net income = Salary - Debt repaymeny obligation

Therefore, net income = $121,899.44 - $20,000 = $101,899.44

Her net income or spending power should be discounted to today's value.

In order to do that, we will use the risk free rate as discounting rate.

Present Value = Future Value / (1+r)^n

PV = 101,899.44 / (1+0.03) ^ 10

Therefore, PV = $75,822.75

Her spending power in today's value is $75,822.75

Answer 2.

If the inflation rate is not given, then I would use the Annual rates of inflation of the Consumer Price Index published by the Labor Department’s Bureau of Labor Statistics (BLS).

Current US CPI inflation rate = 2.5%

If interest rate is not given, then I would use the risk free rate ie. US Treasury Bill rate as given by the US Department of Treasury.

Current US T-Bill annual coupon equivalent rate = 1.56%

Using these rates, same procedure as done for Q1 would be followed.