Question

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Break-Even Investment Returns Your financial planner offers you two different investment plans. Plan X is a $15,000 annual perpetuity. Plan Y is a 10-year, $26,000 annual annuity. Both plans will make their first payment one year from today. At what discount rate would you be indifferent between these two plans?

Answer 1

An annuity is a fixed periodic annual payment over a specified period. It is the continuous cash flow for a fixed period of time. Present value of an annuity is the beginning value of a flow of equal payments.

or Present value of annuity is the today’s value of expected future cash flow of equal payments. Suppose, if an investor wants to know the present value of future payment series, he can use the present value of an ordinary annuity. It will be calculated as follows:

Where:

Present value of an ordinary annuity is defined as PVA

Payment amount is defined as PMT

Interest rate is defined as i

Number of period is defined as n.

Perpetuity is a chain of payments of a fixed amount which continue for an indefinite period of time. Present value of perpetuity is calculated as follows:

Where:

Present value is defined as PV

Payment amount is defined as C

Interest rate is defined as r

Here the requirement is to calculate the interest rate at which an annuity and perpetuity both are indifferent. So for this purpose, it is required to finding the PV of the two options and set them equal to each other.

So first, calculate the PV of perpetuity:

And calculate the PV of annuity which has $26,000 payment each year for 10 years:

Now by setting both the PV and solving for r:

Therefore, the rate is