Question

You are considering purchasing a $1,000 bond with a coupon rate of 9.5%, interest payable annually. You estimate that you will be able to sell the bond at $1,055 after 3 years.

a. If the current inflation rate is 5% per year, which will continue in the foreseeable future, what would be the real rate of return for your investment?

b. If you have determined an 8% inflation-free MARR, what should be the maximum inflation rate so that your investment would be successful?

Answer 1

A)Return on bond is same as it's coupon rate. So annual return given by this bond is 9.5%.

Also at the end of third year, bond will get sold at 1,055 or profit of $55.

So nominal return on investment is (1000 x 9.5% x 3 + 55)/ 1000 = (3 x 95 + 55)/ 1000 = (285+ 55)/1000 =340/1000 =. 34.0%

Since, inflation rate is 5% per year,. These retuns have to be discounted for inflation.

So real rate of return will be( 95/(1.05) + 95/(1.05)^2 +(95+55)/1.05^3 )/1000

= (90.48 + 86.17 +82.06 + 47.51)/1000 = 306.22/1000 = 30.622%.

B) Accepted Inflation free MARR is 8%. As annual return is 9.5%, after inflation adjustment it should not be less than 8%.

Let inflation be i%.

So 9.5%/(1+i%) should be ≥ 8%

Or (1+i%) should be ≤ 9.5%/8.0% or i% should be ≤ 9.5%/8.0% -1

Or i% should be ≤ 1.1875 - 1 = .1875 or 18.75%

Therefore, for successful investment, inflation should be less than 18.75%.

Thanks