Answer:
The value of the investment to you today is $441,751.52.
Note: The correct answer is is $441,751.52 but this is not included in the option. Kindly confirm the correct answer again from your teacher.
Explanation:
This can be determined using the following 5 steps:
Step 1. Calculation of today's of $28,000 per year for the first 4 years
This can be calculated using the formula for calculating the present value of an ordinary annuity as follows:
PV28,000 = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)
Where;
PV28000 = Present value or today's value of of $28,000 per year for the first 4 years = ?
P = Annual payment = $28,000
r = Annual discount return rate = 12%, or 0.12
n = number of years = 4
Substitute the values into equation (1) to have:
PV28,000 = $28,000 * ((1 - (1 / (1 + 0.12))^4) / 0.12)
PV28,000 = $85,045.78
Step 2. Calculation of today's of $43,000 per year for the next 12 years
Present value at year 4 can first be calculated using the formula for calculating the present value of an ordinary annuity as follows:
PV after 4 = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (2)
Where;
PV at 4 = Present value at year 4 = ?
P = Annual payment = $43,000
r = Annual discount return rate = 12%, or 0.12
n = number of years = 12
Substitute the values into equation (2) to have:
PV at 4 = $43,000 * ((1 - (1 / (1 + 0.12))^12) / 0.12)
PV at 4 = $266,358.09
Therefore, we have:
PV43000 = PV at 4 / (1 + r)^n .............................. (3)
Where;
PV43000 = Present value or today's value of of $43,000 per year for the first 12 years = ?
PV at 4 = $266,358.09
r = Annual discount return rate = 12%, or 0.12
n = number of years = 4
Substitute the values into equation (3) to have:
PV43000 = $266,358.09 / (1 + 0.12)^4
PV43000 = $169,275.38
Step 3. Calculation of today's of $69,000 per year for the next 16 years
Present value at year 12 can first be calculated using the formula for calculating the present value of an ordinary annuity as follows:
PV after 12 = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (4)
Where;
PV at 12 = Present value at year 12 = ?
P = Annual payment = $69,000
r = Annual discount return rate = 12%, or 0.12
n = number of years = 16
Substitute the values into equation (4) to have:
PV at 12 = $69,000 * ((1 - (1 / (1 + 0.12))^16) / 0.12)
PV at 12 = $481,205.04
Therefore, we have:
PV69000 = PV at 12 / (1 + r)^n .............................. (5)
Where;
PV69000 = Present value or today's value of of $69,000 per year for the first 16 years = ?
PV at 12 = $481,205.04
r = Annual discount return rate = 12%, or 0.12
n = number of years = 12
Substitute the values into equation (5) to have:
PV69000 = $481,205.04 / (1 + 0.12)^12
PV69000 = $123,513.35
Step 4. Calculation of today's of $61,000 per year for the next 13 years
Present value at year 16 can first be calculated using the formula for calculating the present value of an ordinary annuity as follows:
PV after 16 = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (6)
Where;
PV at 16 = Present value at year 16 = ?
P = Annual payment = $61,000
r = Annual discount return rate = 12%, or 0.12
n = number of years = 13
Substitute the values into equation (6) to have:
PV at 16 = $61,000 * ((1 - (1 / (1 + 0.12))^13) / 0.12)
PV at 16 = $391,836.45
Therefore, we have:
PV61000 = PV at 16 / (1 + r)^n .............................. (7)
Where;
PV61000 = Present value or today's value of of $61,000 per year for the first 13 years = ?
PV at 16 = $391,836.45
r = Annual discount return rate = 12%, or 0.12
n = number of years = 16
Substitute the values into equation (7) to have:
PV69000 = $391,836.45 / (1 + 0.12)^16
PV69000 = $63,917.01
Step 5. Calculation of the value of the investment to you today
This can be calculated by adding the values above:
PV = PV28,000 + PV43000 + PV69000 + PV69000 = $85,045.78 + $169,275.38 + $123,513.35 + $63,917.01 = $441,751.52
Therefore, the value of the investment to you today is $441,751.52.
