Question

You can buy property today for $3 million and sell it in 5 years for $4 million. (you earn no rental income on the property.)
a. if the interest rate is 8%, what is the present value of the sales price? (do not round intermediate calculations. enter your answer in millions rounded to 3 decimal places.)
b. is the property investment attractive to you? yes no c-1. what is the present value of the future cash flows, if you also could earn $200,000 per year rent on the property? the rent is paid at the end of each year. (do not round intermediate calculations. enter your answer in millions rounded to 3 decimal places.) c-2. is the property investment attractive to you now? yes no

Answer 1

a. Rate of interest : 8%

Today’s Price = $3,000,000

Price after 5 years = $4,000,000

Present Value of price after 5 years = $4,000,000 / (1+0.08)^5

= $2,722,333.88

b. The property is not worth investing, since investing in the land is $3,000,000 while it can be sold today as $2,722,333, thus not a profitable investment as it will incur a loss of $277,667 ($3,000,000 - $4,000,000).

c. Present value of rent of 5 Years = $200,000*PVIFA(8%,5)

= $200,000*3.99999

= $798,542.01

d. NET PRESENT VALUE OF INVESTMENT = PRESENT VALUE OF FUTURE CASH FLOWS – INITIAL INVESEMTENT

NET PRESENT VALUE = $2,722,333.88 + $798,542.01 - $3,000,000

NET PRESENT VALUE = $520,874.80

Since the Net Present value is positive, it is worth investing in the land.

Answer 2

The present value tells if the amount of money today has more than the same amount in the future. Thus, the investment looks attractive if along with present value of future cashflows, rent is also added.

What is the present value of future cashflows?

Present value (PV) is the present value of future cash flows or cash flows given a specified amount of return. Upcoming cash flows are discounted at a discounted rate, and when the discount rate is high, the current cash flow rate decreases.

As per the given information,

a)Present value of the sales price can be calculated as below:

$\rm\,Rate = 8\%\\\\Number\,of\,years = 5\,years\\\\Future\,Value (FV) = \ 4,000,000\\ \\Present\,Value = \dfrac{FV}{(1+r)^{n}}\\\\Present\,Value = \dfrac{4,000,000}{(1+0.08)^{5}}\\\\\rm\,Present\,Value = \ 2,722,333.88$

b) As we can observe above, the current value of the property is  $3,000,000.

The sale value of property in the future is $4,000,000 and the present value of the future cash flows is $2,722,333.88 which is a complete loss for the organization as the investment itself is $3,000,000.

C) 1. The present value of future value annuity needs to be calculated for the rent that the person can receive if the house is given for rent.

$\rm\,PV = P\times\,\dfrac{1 -[\dfrac{1}{(1+r)^{n}}]}{r}\\\rm\,PV = \rm\,200,000\times\,\dfrac{1 -[\rm\,\dfrac{1}{(1+0.08)^{5}}]}{\rm\,0.08}\\\\\\\rm\,PV = 200,000\times 3.999\\\\\rm\,PV = \ 798,540.01$

C) 2 . Net present value of investment:

$\rm\,Net\,Value\,of\,Investment = Present\,Value\,of\,Future\Cash\,flows - Initial\,Investment\\\\\\rm\,Net\,Value\,of\,Investment = \, 2,722,333.88 + \ 798,540.0 - 3,000,000\\\\\rm\,Net\,Value\,of\,Investment = \ 520,873.98$

Hence, the property investment looks attractive now.

To learn more about present value of future cash flows, refer the link:

https://brainly.com/question/26371663