Question

3. What is the present value of single cash flow of $25,000 received at the end of 10 years, if we asume a discount rate of 5% annually With a dicount rate of 7%?

Answer 1

Answer:

5% Discount: $14,968.42

7% Discount: $12,099.56

Step-by-step explanation:

Since the discount rate is being compounded annually we can go ahead and use the Exponential Growth Formula, or in this case we will actually be using the Exponential Decay Formula since we are compounding a discount rate

$D = a*(1-r)^{t}$

Where:

1. D is the present value
2. a is the initial cash flow
3. r is the discount rate in decimal form
4. t is the span of time

Since we are looking for the present value in 10 years with a rate of 5%, we can plug these values into the formula and solve for D.

$D = 25000*(1-0.05)^{10}$

$D = 25000*(0.95)^{10}$

$D = 25000*0.5987$

$D = 14,968.42$

So the Present day value at 5% discount rate is $14,968.42 .

Now we can solve the equation at a 7% discount rate.

$D = 25000*(1-0.07)^{10}$

$D = 25000*(0.93)^{10}$

$D = 25000*0.48398$

$D = 12,099.56$

So the Present day value at 7% discount rate is $12,099.56

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