Question

1. What is the value at the end of Year 3 of the following cash flow stream if interest is 4% compounded semiannually? (Hint: You can use the EAR and treat the cash flows as an ordinary annuity or use the periodic rate and compound the cash flows individually.) Please list the inputs of your financial calculator.

0 2 4 6 Periods

                           | | | | | | |

                          0 200 200 200

2. What is the PV? Please list the inputs of your financial calculator

3. What would be wrong with your answer to part (2) if you used the nominal rate, 4%, rather than the EAR or the periodic rate, INOM/2 = 4%/2 = 2% to solve the problems? Would the present value be overstated or understated?

Answer 1

1.)

2 period = 1 year

4% compounded semi-annually is equivalent to ((1+0.04/2)^2) - 1 = 4.04% annually

Inputing the values in a financial calculator for Future value (FV)

PV = 0

PMT= -200

N=3

I/Y = 4.04

CPT FV, we get FV = 624.566

2.)

For present value PV, we input the following in a financial calculator

PMT = -200

N=3

I/Y = 4.04

FV= 0

CPT PV, we get PV = 554.5971

3.)

If we had used the nominal rate of 4%, the PV would be

PMT = -200

N=3

I/Y = 4

FV= 0

CPT PV, we get PV = 555.0182

Hence, we would had overstated the present value by (555.0182-554.5971) =0.4211