Real-Life Math -- Solution
You know that the discount rate (I) is 15 percent. Knowing that, you can figure out the discount factor for the first year (N being the number of years):
Discount factor = 1 / [(1 + I)N]
Discount factor = 1 / [(1 + 0.15)1]
Discount factor = 1 / 1.15
Discount factor = 0.87, or 87 percent
You made $120,000 in sales in the first year. But now you have to account for the discount factor.
Present value = $120,000 x 0.87
Present value = $104,400
Now do your calculations for the second year:
Discount factor = 1 / [(1 + I)N]
Discount factor = 1 / [(1 + 0.15)2]
Discount factor = 1 / 1.152
Discount factor = 1 / 1.32
Discount factor = 0.75
Present value = $140,000 x 0.75
Present value = $105,000
And for the third year:
Discount factor = 1 / [(1 + I)N]
Discount factor = 1 / [(1 + 0.15)N]
Discount factor = 1 / [1.153]
Discount factor = 1 / 1.52
Discount factor = 0.66
Present value = $160,000 x 0.66
Present value = $105,600
TOTAL PRESENT VALUE = $104,400 + $105,000 + $105,600
TOTAL PRESENT VALUE = $315,000
So the total present value of the property is $315,000.
| Year | Sales | Extra Sales | Total Sales | Discount Factor | Present Value |
| 1 | 100,000 | 20,000 | 120,000 | 0.87 | 104,400 |
| 2 | 120,000 | 20,000 | 140,000 | 0.75 | 105,000 |
| 3 | 140,000 | 20,000 | 160,000 | 0.66 | 105,600 |
| Total Present Value | | | | | 315,000 |