Question

A real estate investment has the following expected cash flows:

	Year 0	Year 1	Year 2	Year 3	Year 4
Cashflow		10,000	25,000	50,000	35,000

The discount rate is 9%. What is the investment’s value 4 years from now?

Select one:

a. $ 132,152

b. $103,700

c. $ 113,345

d. $120,000

e. $130,757

Answer 1

Given information in question is Cash flows from real estate investment from year 1 to year 4.
Assuming Investment is made in Year 0.
Our objective is to calculate the value of the investment at the end of the 4th Year.

Cash flows are as follows

Year	Year 0	Year 1	Year 2	Year 3	Year 4
Cash Flow		10000	25000	50000	35000

Given Discount Rate ( r ) 9%.

First, we are going to calculate discounted cash flows for each year.

This will give us the value of the investment in Year 0. Then we will use the compound interest formula to calculate the value of the investment in 4 years.

The formula used for calculation of discounted cash flows is the Present Value (PV) formula
PV = Cash Flow / (1+r)^n
Where r is the discount rate and "n" is the period ( in this question that is in years )

Compound interest formula
A= P*(1+r )^n where A is the Final amount, P is the initial principal amount, r is the rate of interest, and n is the number of periods.
Note:- Always keep in mind if the period is in years then "r" should also be annual rate.

So Using PV formula

PV of Year 1= 10000 / (1+9%)^1 = 9174

PV of Year 2= 25000 / (1+9%)^1 = 21042

PV of Year 3= 50000 / (1+9%)^1 = 38609

PV of Year 4= 35000 / (1+9%)^1 = 24795

So total PV = 93620 ( Sum of above 4 values )

Present value means value of investment in year 0.

Now we have to calculate the value of investment after 4 years using compund interest formula. ( rate of compounding remains same as discount rate
P= 93620, r = 9%, n = 4

Investment Value after 4 yeas r= 93620*(1+9%)^4 = 132152.

So the answer is $132152.

Value of investment will be $132152 after 4 years with given cash flows.

So the Option "a" is correct.