Answer:
a. The present value of the sales price is $1.657 million.
b. No. This is because an investment in the property will result in a negative net present value (NPV) of $0.443 million.
c-1. The present value of the future cash flows is $2.122 million.
c-2. Yes. Yes. This is because an investment in the property will result in a positive net present value (NPV) of $0.022 million.
Explanation:
Note: This question is not complete. The complete question is therefore presented before answering the question as follows:
You can buy property today for $2.1 million and sell it in 6 years for $3.1 million. (You earn no rental income on the property.)
a. If the interest rate is 11%, 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?
c-1. What is the present value of the future cash flows, if you also could earn $110,000 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?
The explanation to the answers is now provided as follows:
a. If the interest rate is 11%, what is the present value of the sales price? (Do not round intermediate calculations. Enter your answer in millions rounded to 3 decimal places.)
The present value of the sales price can be calculated using the simple present value formula as follows:
PV = FV / (1 + r)^n ……………………….. (1)
Where;
PV = Present value of the sales price = ?
FV = Future value or the sales price in 6 years = $3.1 million
r = interest rate = 11%, or 0.11
n = number of years = 6
Substitute the values into equation (1), we have:
PV = $3.1 / (1 + 0.11)^6
PV = $3.1 / 1.11^6
PV = $3.1 / 1.870414552161
PV = $1.65738659187525 million
Rounding to 3 decimal places, we have:
PV = $1.657 million
Therefore, the present value of the sales price is $1.657 million.
b. Is the property investment attractive to you?
No. This is because an investment in the property will result in a negative net present value (NPV) of $0.443 million.
The negative net present value (NPV) of $0.443 million is determined as follows:
NPV = Present value of the sales price - Acquisition cost = $1.657 million - $2.1 million = -$0.443 million
c-1. What is the present value of the future cash flows, if you also could earn $110,000 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.)
The present value of the future cash flows can be calculated using the following steps:
<u>Step 1: Calculation of the present value of the $110,000 per year rent</u>
Since the rent is paid at end of each year, this can be calculated using the formula for calculating the present value of an ordinary annuity as follows:
PVR = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (2)
Where;
PVR = Present value of yearly rent = ?
P = Annual rent =$110,000
r = interest rate = 11%, or 0.11
n = number of years = 6
Substitute the values into equation (2) to have:
PVR = $110,000 * ((1 - (1 / (1 + 0.11))^6) / 0.11)
PVR = $110,000 * 4.23053785373826
PVR = $465,359.163911209
Converting to million and rounded to 3 decimal places, we have:
PVR = $0.465 million
<u>Step 2: Calculation of the present value of the future cash flows</u>
Present value of future cash flows = Present value sales price + Present value of annual rent ……. (3)
Where;
Present value sales price = $1.657 million, as already calculate in part a above
Present value of annual rent = PVR = $0.465 million
Substituting the values into equation (3), we have:
Present value of future cash flows = $1.657 million + $0.465 million = $2.122 million
Therefore, the present value of the future cash flows is $2.122 million.
c-2. Is the property investment attractive to you now?
Yes. This is because an investment in the property will result in a positive net present value (NPV) of $0.022 million.
The positive net present value (NPV) of $0.022 million is determined as follows:
NPV = Present value of tof the future cash flows - Acquisition cost = $2.122 million - $2.1 million = 0.0219999999999998 million
Converting to million and rounded to 3 decimal places, we have:
NPV = $0.022 million