Question

Suppose that you are going to receive two payments of $500, the first at the end of year 3, and the other at the end of year 6.

1. First, draw the time line and mark the time (years) and payments on the timeline.
2. How much are you willing to pay for those cash flows (CFs) today if the current discount rate is 5%?
3. What if the discount rate is 6% instead?
4. How much would you be willing to pay in at the end of year 1 if the discount rate is 5%?
5. How much would you be willing to pay in at the end of year 2 using the same 5% discount rate?

show both formula and with financial calculator

Answer 1

Payment 1 , at the end of 3rd year,p1 = $500

payment 2, at the end of 6th year ,p2= $500

amount willing to pay today = present value of the cash flows

interest rate = r = 5% = 0.05

present value = [p1/((1+r)³ )] + [p2/((1+r)⁶ )] = [500/((1.05)³ )] + [500/((1.05)⁶ )] = 431.91879 + 373.10769 = 805.02648 = 805.03 (after rounding off to 2 decimal places)

if r = 6%

present value = [500/((1.06)³ )] + [500/((1.06)⁶ )] = 419.80964 + 352.48027 = 772.28991 or 772.29

USING Financial Calculator;

1) enter the value 3 , then press N.

2) enter the value , 5 , then press I (for interest rate)

3) enter the value 500, then press FV.

4) then press CPT PV , to get the present value

this will give you the present value of the amount 500 at the end of 3rd year

similarly calculate the present value of the 2nd cash flow using the above steps, by just replacing the value of N by 6 since the payment is received at the end of 6th year

then to get the final answer, just add the 2 values you got using the above steps.

to calculate the present value for interest rate of 6%, follow the same steps as above and just change./ replace the value of I by 6 ( for interest rate of 6%)