Examples
Problem:
Suppose you invest $10,000 today in an account that pays 5% interest, compounded annually, how much will you have in the account at the end of 6 years?
Solution: $13,401
| 10000 | CHS | PV |
| 5 | i | |
| 6 | n | |
| FV |
Problem:
Suppose you are promised annual payments of $1,500 each year for the next five years, with the first cash flow occurring in one year. If the interest rate is 4%, what is this stream of cash flows worth today?
Solution: $6,678
| 1500 | PMT | |
| 5 | n | |
| 4 | i | |
| PV |
Problem:
Calculate the value of a bond with a maturity value of $1,000, a 5% coupon (paid semi-annually), five years remaining to maturity, and is priced to yield 8%.
Solution: $878.34
Note:
FV = 1,000 (lump-sum at maturity)
CF = $25 (one half of 5% of $1,000)
N = 10 (10 six-month periods remaining)
i = 4% (six-month basis, 8%/2)
| 1000 | FV |
| 10 | n |
| 4 | i |
| 25 | PMT |
| PV |
Problem:
Consider the following cash flows,
CF0 = -$10,000
CF1 = +$5,000
CF2 = $0
CF3 = +$2,000
CF4 = +$5,000
Solution:
| 10000 | CHS | g | CF0 |
| 5000 | g | CFj | |
| 0 | g | CFj | |
| 2000 | g | CFg | |
| 5000 | g | CFg | |
| f | IRR | ||
| 5 | i | ||
| f | NPV |
Problem:
Calculate the yield to maturity of a bond with a maturity value of $1,000, a 5% coupon (paid semi-annually), ten years remaining to maturity, and is priced $857.
Solution: 7.01%
Note:
FV = $1,000 (lump-sum at maturity)
CF = $25 (one half of 5% of $1,000)
N = 20 (20 six-month periods remaining)
PV = $857
| 1000 | FV | |
| 20 | n | |
| 857 | CHS | PV |
| 25 | PMT | |
| i | ||
| 2 | x |