Question

You expect to receive a payment of $\$104$one year from now.

a. Your rate of discount is $4$percent. What is the present value of the payment to be received?

b. Suppose that your rate of discount rises to $5$percent. What is the present value of the payment to be received?

Short answer

a. The present value of the payment to be received is $\$100$.

b. the future value is remained same.

Step-by-step solution

Introduction

Economic rent refers to additional payments made to or for a factor of production over and beyond the amount expected by its owner.

The discount rate is the rate of interest used in discounted future cash flow (DCF) analysis to determine the present value of future cash flows.

Given Information (Part a)

a) By using an interest rate of$\%$, the annual payout that is expected today$\$104$

Explanation ( Part a)

The following is the present value of the payment to be received:

$P{V}_t=\frac{F{V}_1}{1+i}$

$"P{V}_t"$reflects the one-year present value of a sumlocalid="1653218126782" $"F{V}_t"$represents the total amount paid or collected over the course of a year, and$"i"$describes the current interest rate on the marketplace.

$P{V}_t=\frac{104}{1+0.04}$

$P{V}_t=\frac{104}{1.04}$

$P{V}_1=100$

The expected payout has a present value of$\$100.$

Given Information (Part b)

b) If the discount rate is increased to, the present value will be as follows:$5$percent.

Explanation (Part b)

Whereas if discounting price is higher to$5$ percent, the current value would be as followed.

$P{V}_t=\frac{104}{1+0.05}$

$P{V}_t=\frac{104}{1.05}$

$P{V}_t=99.04$

The present value would be $\$99.04$if the future value remained the same, i.e. $\$104$, and the discount rate was increased to $5$percent.