4.1 NOTE: Please show all calculations (no Excel solutions please) to four decim

Question

4.1

NOTE: Please show all calculations (no Excel solutions please) to four decimal places if applicable: Assume that the correct discount rate for the following cash flows is 8%. What is the present value of the following cash flows?

a.

$50 at the end of 3 years

b.

$50 at the end of 100 years

c.

$50 received at the end of each year for 20 years

d.

$50 received at the beginning of each year, totaling 20 payments.

4.1

NOTE: Please show all calculations (no Excel solutions please) to four decimal places if applicable: Assume that the correct discount rate for the following cash flows is 8%. What is the present value of the following cash flows?

a.

$50 at the end of 3 years

b.

$50 at the end of 100 years

c.

$50 received at the end of each year for 20 years

d.

$50 received at the beginning of each year, totaling 20 payments.

Explanation / Answer

PV of CFs = FV/(1+i)^n where i is the Disc rate & n is the period in years a. PV of CF = 50/(1+8%)^3 = $39.69 b. PV of CF = 50/(1+8%)^100 = $0.02 c. Here it is PV of annuity for n=20 & PMT=$50 SO PVA = PMT*(PVIFAi,n) ie PVA = $50*(PVIFA8%,20). From PV of annuity Table, we get (PVIFA8%,20) = 9.8181 So PVA = 50*9.8181 = $490.91 d. PV of Annuity due = PVA =(1+i)*PMT*(PVIFAi,n) ie PVA = $50*(PVIFA8%,20)*(1+8%) From PV of annuity Table, we get (PVIFA8%,20) = 9.8181 So PVA = 50*9.8181*1.08 = $530.18

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