Examples

1. Calculating a future value
2. Calculating the present value of an annuity
3. Calculating the value of a bond
4. Valuing a series of uneven cash flows
5. Calculating the yield to maturity on a bond

1. 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: $13,401

   10000	CHS	PV
   5	i
   6	n
   FV

    

2. 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: $6,678

   1500	PMT
   5	n
   4	i
   PV

    

3. 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: $878.34

   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

    

4. Valuing a series of uneven cash flows

   Problem:

   Consider the following cash flows,

   CF₀ = -$10,000
   CF₁ = +$5,000
   CF₂ = $0
   CF₃ = +$2,000
   CF₄ = +$5,000

   1. What is the internal rate of return for this set of cash flows?
   2. If the discount rate is 5%, what is the net present value corresponding to these cash flows?

   Solution:

   1. IRR = 7.5224%
   2. NPV = +$603.09

   10000	CHS	g	CF0
   5000	g	CFj
   0	g	CFj
   2000	g	CFg
   5000	g	CFg
   f	IRR
   5	i
   f	NPV

    

5. 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 = $857

   1000	FV
   20	n
   857	CHS	PV
   25	PMT
   i
   2	x