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

Question

4.3

NOTE: Please show all calculations (no Excel solutions please) to four decimal places if applicable: Calculate the following values, assuming a discount rate of 8%:

a.

present value of a perpetuity (also called a perpetual annuity) of $50 received each year at the end of each year

b.

present value of an annuity of $50 received at the end of each year for 5 years

c.

present value of an annuity of $50 received at the end of each year for 10 years, with the first payment to be received at the end of the 6th year

d.

present value of a perpetuity of $50, with the first payment received at the end of the 16th year.

4.3

NOTE: Please show all calculations (no Excel solutions please) to four decimal places if applicable: Calculate the following values, assuming a discount rate of 8%:

a.

present value of a perpetuity (also called a perpetual annuity) of $50 received each year at the end of each year

b.

present value of an annuity of $50 received at the end of each year for 5 years

c.

present value of an annuity of $50 received at the end of each year for 10 years, with the first payment to be received at the end of the 6th year

d.

present value of a perpetuity of $50, with the first payment received at the end of the 16th year.

Explanation / Answer

a. PV of perpetuity = A/i where A is annual payment & i is disc rate SO PV of Perpetuity = 50/8% = $625.00 b. Here it is PV of annuity for n=5 & PMT=$50 SO PVA = PMT*(PVIFAi,n) ie PVA = $50*(PVIFA8%,5). From PV of annuity Table, we get (PVIFA8%,5) = 4.3295 So PVA = 50*4.3295 = $216.48 c. This has 2 parts. First Find teh PV of Annuity at 6 yrs & then find the PV of that AMount at T0. Here it is PV of annuity for n=10 & PMT=$50 SO PVA = PMT*(PVIFAi,n) ie PVA = $50*(PVIFA8%,10). From PV of annuity Table, we get (PVIFA8%,5) = 6.7101 So PVA = 50*6.7101 = $335.51 Now PV = FV/(1+i)^n = $335.51/(1+8%)^6 = $211.43 d. This has 2 parts. First Find teh PV of Perpetuity at 16 yrs & then find the PV of that AMount at T0. PV of Perpetuity = A/i = 50/8% = $625 Now PV of this amount PV = 625/(1+8%)^16 = $182.43

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