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?

Is the below method correct, if not please advise.

a.

First find Nominal Interest Rate Rate of Return

0 = -1000 + (1000*.95) (p/a, i%, 3) + 1055(p/f, i%,3)

Try i = 8 %, where (p/a, 8%, 3) = 2.5770 and (p/f, 8%,3) = .7938 which results in 82.31

Try i = 12% where (p/a, 12%, 3) = 2.4018 and (p/f, 12%,3) = .7117 which results in -20.89

Now interpolate and find nominal interest rate i = 11.19%

Then use the formula (1 + i) = (1 + r) (1 + f) where the nominal rate i = 11.19 %, the inflation rate f = 5%, and find real rate r.

So: (1 + .1119) = (1 + r) (1 + .05) = > r = 5.89%

Real Rate of Return on investment = 5.89%

b.

To find max inflation rate use the formula (1 + i) = (1 + r) (1 + f) where the nominal rate i = 11.19 %, real rate r = 8%, and find the inflation rate f.

So: (1 + .1119) = (1 + .08) (1 + f) => f = 2.95%

To achieve a MARR of 8% the max inflation = 2.95%

Is this correct, if not please advise.

Answer 1

A: Find nominal rate of return using financial calculator

Input: Pv=-1000, PMT=9.5%*1000=95, FV=1055, N=3

Find I/Y = 11.14%

This is the Nominal rate

(1 + i) = (1 + r) (1 + f)

(1+0.1114)= (1+r)*(1+0.05)

r=5.85%

b: (1 + i) = (1 + r) (1 + f)

(1+0.1114)= (1+0.08)*(1+r)

(1+r) = 1.029074

r=2.91%