Question

QUESTION 33 Listed below are five different cash flow bundles. If your discount rate is 13% (annual compounding), which bundle has the greatest present value? Five annual payments of $2,800- the first payment occurs one year from today. A perpetual stream of annual payments starting at $500 in one year and increasing at 5% per year thereafter. ОО A lump sum payment of $10,000 today. A perpetual stream of annual payments of $1,000 starting in one year, О A lump sum payment of $25,000 at the end of 10 years.

Answer 1

Here we need to find present value of all the option
option 1) Five annual payments of $ 2800
PV = Annuity xPVIFA(r%,n)
r = rate of interest = 13%
n = no. of payments = 5
PVIFA(r% , n) = [1-(1/(1+r)^n) / r ]
PVIFA(13% , 5) = [ 1-(1/(1+13%)^5 / 13%]
= [ 1 -(1/(1+0.13)^5 / 0.13]
=[1-(1/(1.13)^5 / 0.13]
=[1-0.54276 / 0.13]
=[0.45724/0.13]
=3.5172

Thus PV = 2800 x 3.5172
= $9848.25

Option 2) Perpetual stream of $500 in one year with growth rate = 5%
PV = Annuity(Required rate of return - growth rate)
= 500/(13%-5%)
= 500/8%
= $6250

Option 3) Lumpsum payment today = $10,000
Here PV = $10,000

Option 4) Perpetual stream of $1000 in one year
PV = Annuity/Required rate of return
= 1000/13%

=7692.31 $

Option 5) Lumpsum payment at end of 10 years
PV = 25000/(1+r)^n
= 25000/(1+13%)^10
=25000/(1.13)^10
= 25000/3.394567
= $7364.71

Thus Option 3) has greatest present value