Question

4. Suppose you can have option A: $3,000 today, or option B: $10,000 in 10 years. Which option do you take? Use 12% for discounting (or 12% for your interest rate). At what interest rate (be specific!) are you indifferent about making the two choices? 5. Imagine you buy a bond, priced at $1,000. This bond pays $50 in interest every year and in the fifth year it pays the $50 in interest plus the return of the $1,000 principle. The cashflows for the 5 years are given as follows: Initial Investment (Co) $1,000 Year 1 $50 Year 2 $50 Year 3 $50 Year 4 $50 Year 5 $1,050 Using 8% for discounting, what is the net present value (NPV) of this investment? Find the internal rate of return (IRR). If you suddenly decide you are ok with a 4% return, do you make the initial investment? At what interest rate (be specific!) are you indifferent about making the initial investment?

Answer 1

4]

The present value of $3,000 received today is $3,000 itself, since it is received immediately today.  

The value of $10,000 received after 10 years is calculated as below :

present value = future value / (1 + interest rate)^{number of years}

present value = $10,000 / (1 + 12%)¹⁰

present value = $3,219.73

The present value of $10,000 received after 10 years is $3,219.73.

I would take the option of receiving $10,000 after 10 years because its present value is higher than the $3,000 that can be received today.

If you are to be indifferent the present value of $10,000 received after 10 years should equal $3,000 which can be received today.

present value = future value / (1 + interest rate)^{number of years}

Let us say the interest rate is R.

$3,000 = $10,000 / (1 + R)¹⁰

R = ($10,000 / $3,000)^1/10 - 1

R = 0.1279, or 12.79%.

The interest rate at which indifference occurs is 12.79%