In: Economics
b. Suppose that interest rates are 10%. You have the option to buy an asset that pays $100 per year for 30 years. If all you cared about is the present value of payments this asset generated how much would you be willing to pay to acquire this asset. Assume that there is no uncertainty about the payments one would receive over the 30 year period.
We would be willing to pay anything equal to less than the present value of $100 with a 10% interest rate.
Present value is the value in the present, of a sum of money, in contrast to some future value it will have when it has been invested at compound interest.
Present value = Future value/(1+interest rate)*time
For first payment
= 100(1+10%)*1
= $90.91
For 2nd payment
= 100(1+10%)*2
= $82.64
For 3rd payment
= 100(1+10%)*3
= $75.13
For 4th payment
= 100(1+10%)*4
= $68.30
For 29th payment
= 100(1+10%)*29
= $6.30
For 30th payment
= 100(1+10%)*30
= $5.73
In the table form:
Year | Payments | PV |
1 | $100 | $90.91 |
2 | $100 | $82.64 |
3 | $100 | $75.13 |
4 | $100 | $68.30 |
5 | $100 | $62.09 |
6 | $100 | $56.45 |
7 | $100 | $51.32 |
8 | $100 | $46.65 |
9 | $100 | $42.41 |
10 | $100 | $38.55 |
11 | $100 | $35.05 |
12 | $100 | $31.86 |
13 | $100 | $28.97 |
14 | $100 | $26.33 |
15 | $100 | $23.94 |
16 | $100 | $21.76 |
17 | $100 | $19.78 |
18 | $100 | $17.99 |
19 | $100 | $16.35 |
20 | $100 | $14.86 |
21 | $100 | $13.51 |
22 | $100 | $12.28 |
23 | $100 | $11.17 |
24 | $100 | $10.15 |
25 | $100 | $9.23 |
26 | $100 | $8.39 |
27 | $100 | $7.63 |
28 | $100 | $6.93 |
29 | $100 | $6.30 |
30 | $100 | $5.73 |
Total | $3,000.00 | $942.69 |
So we are willing to pay 942.69 or less for this asset.