Examples

## Calculating a future value

**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:**$13,40110000 CHS PV 5 i 6 n FV ## Calculating the present value of an annuity

**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:**$6,6781500 PMT 5 n 4 i PV ## Calculating the value of a bond

**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:**$878.34Note:

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 ## Valuing a series of uneven cash flows

**Problem:**Consider the following cash flows,

CF

_{0}= -$10,000

CF_{1}= +$5,000

CF_{2}= $0

CF_{3}= +$2,000

CF_{4}= +$5,000- What is the internal rate of return for this set of cash flows?
- If the discount rate is 5%, what is the net present value corresponding to these cash flows?

**Solution:**- IRR = 7.5224%
- NPV = +$603.09

10000 CHS g CF _{0}5000 g CF _{j}0 g CF _{j}2000 g CF _{g}5000 g CF _{g}f IRR 5 i f NPV ## Calculating the yield to maturity on a bond

**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 = $8571000 FV 20 n 857 CHS PV 25 PMT i 2 x