Assuming discount rate-present value of a perpetuity

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Reference no: EM13917531

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 PV of perpetuity = A/i where A is annual payment and i is disc rate SO PV of Perpetuity = 50/8% = $625.00 b. present value of an annuity of $50 received at the end of each year for 5 years Here it is PV of annuity for n=5 & PMT=$50 PVA = PMT*(PVIFAi,n) PVA = $50*(PVIFA8%,5). From PV of annuity Table, we get (PVIFA8%,5) = 4.3295 So PVA = 50*4.3295 = $216.48 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 This has 2 parts. First Find the 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) i.e. 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. present value of a perpetuity of $50, with the first payment received at the end of the 16th year This has 2 parts. First Find the 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 (8 marks) 4.4 a. Show (with a time line, for example) that the perpetuity in 4.3a. is exactly the same as the sum of the annuities and perpetuities in 4.3b. to 4.3d. Can I please get an answer dor 4.4 a?

Reference no: EM13917531

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