4.3 Need help with 4.4 a and b at bottom. 4.3 is required to answer this. Calcul
ID: 2669743 • Letter: 4
Question
4.3
Need help with 4.4 a and b at bottom. 4.3 is required to answer this.
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.
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)
i.e. 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 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. 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
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.
b.
Show that their present values add up to the same amount.
4.3
Need help with 4.4 a and b at bottom. 4.3 is required to answer this.
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.
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)
i.e. 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 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. 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
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.
b.
Show that their present values add up to the same amount.
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 ...............Ans (a) b. Here it is PV of annuity for n=5 & PMT=$50 SO PVA = PMT*(PVIFAi,n) i.e. PVA = $50*(PVIFA8%,5). From PV of annuity Table, we get (PVIFA8%,5) = 3.9927 So PVA = 50*3.9927 = $199.64 .....Ans (b) c. 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%,10) = 6.7101 So PVA = 50*6.7101 = $335.51 Now PV = FV/(1+i)^n = $335.51/(1+8%)^5 = $228.34 ..Ans (C) d. 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%)^15 = $197.03 ..Ans (d) 4.4b : Prove a = b+c+d From ABove, we have a=$625 & b+c+d = $199.64 + $228.34+ $197.03 = $625.00 ..................Proved
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