Exercise C-6: Calculate the Present Value of a Single Amount

Ray and Rachel are considering the purchase of two deluxe kitchen ovens. The first store offers the two ovens for $3,200 with payment due today. The second store offers the two ovens for $3,400 due in one year.

Required:

1-a. Assuming an annual discount rate of 9%, calculate the present value of the $3,400 payment due in one year.

1-b. From which store should Ray and Rachel buy their ovens?

The first store offers the price of $3,200 with payment due today, the second offers the price of $3,400 due in one year. With discount rate 9%, the present value of the second store's offer is $3,119.27. Hence, the couple should buy from the second store because it is cheaper.

The discount rate can be thought of as the percentage of return on investment that you could have received if you had received that dollar today.

The relation between discount rate and the present value is given in the following formulas:

DF = 1 / (1 + d)ⁿ

PV = DF x cash flow

Where:

DF = discount factor

d = discount rate

n = number of periods

PV = present value

First store offer: The present value is $3,200 since the payment due today

Second store offer:

DF = 1 / (1.09) = 0.917

PV = DF x 3,400 = 0.917 x 3,400 = 3,119.27

The offer from the second store has less present value, which means the price in the present day is cheaper compared to the offer from the first store. Hence, the couple should buy from the second store.

Learn more about discount rate at:

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