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.
Step-by-step 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:
Step 1: Calculation of the present value of the $110,000 per year rent
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
Step 2: Calculation of the present value of the future cash flows
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