Consider the following two cash flow series of payments Seri

Consider the following two cash flow series of payments: Series A is a geometric series increasing at a rate of 11% per year. The initial cash payment at the end of year 1 is $1,000. The payments occur annually for 5 years. Series B is a uniform series with payments of value X occurring annually at the end of years 1 through 5. You must make the payments in either Series A or Series B.

If your TVOM is 8%, would you be indifferent between these two series of payments? Enter the PW for each series to support this choice.

Solution

(1) For series A, effective discount factor = 1.11 / 1.045 = 1.0622

PW of series A = $1,000 x PVIFA (6.22%, 5 years) = $1,000 x 4.1873 [From PVIFA calculator] = $4,187.30

For equivalence,

$4,187.3 = X. PVIFA (4.5%, 5 years) = X. 4.39 [From PVIFA calculator]

X = $4,187.3 / 4.39 = $953.83

(2) For series A, effective discount factor = 1.11 / 1.08 = 1.0278

PW of series A = $1,000 x PVIFA (2.78%, 5 years) = $1,000 x 4.6086 [From PVIFA calculator] = $4,608.6

For equivalence,

$4,608.6 = X. PVIFA (8%, 5 years) = X. 3.9927 [From PVIFA calculator]

X = $4,608.6 / 3.9927 = $1,154.26

(3) For series A, effective discount factor = 1.11 / 1.05 = 1.0571

PW of series A = $1,000 x PVIFA (5.71%, 5 years) = $1,000 x 4.2458 [From PVIFA calculator] = $4,245.8

For equivalence,

$4,245.8 = X. PVIFA (5%, 5 years) = X. 4.3295 [From PVIFA calculator]

X = $4,245.8 / 4.3295 = $980.67