Question

Given a discount rate of 11%, which of the following cash flow streams has the highest present value?

Multiple Choice

• 12 equal payments of $600 beginning at the end of Year 1.

• 10 equal payments of $600 beginning immediately.

• 12 equal payments of $550 beginning immediately.

Answer 1

> Formula

Present Value = Future Value / ( 1 + r )n

PVAF(r, n) = Present Value Annuity Factor

                  = [ 1/(1+r) + 1/(1+r)1 + 1/(1+r)2 + ...... + 1/(1+r)n ]

> Calculation

Option 1 - 12 payment of $ 600 beginning at the end of year 1

Present Value = Cash flow * PVAF (r, n)

                       = 600 * PVAF(11%, 12 )

                      = 600 * [ (1/1.11) + 1/1.11)2 +......+ 1/1.11)12 ]

                      = 600 * 6.492356

                       = 3895.41 Answer

Option 2 - 10 payment of $ 600 beginning at the start of year 1

Present Value = Cash flow at year 0 + Cash flow * PVAF (r, n)

                       = 600 + 600 * PVAF(11%, 9 )

                      = 600 + 600 * [ (1/1.11) + 1/1.11)2 +......+ 1/1.11)9 ]

                      = 600 + 600 * 5.537048

                       = $ 3922.23 Answer

Option 3 - 12 payment of $ 550 beginning at the start of year 1

Present Value = Cash flow at year 0 + Cash flow * PVAF (r, n)

                       = 550 + 550 * PVAF(11%, 11 )

                      = 550 + 550 * [ (1/1.11) + 1/1.11)2 +......+ 1/1.11)11 ]

                      = 550 + 550 * 6.206515

                       = $ 3963.58 Answer

> Answer

The present value is highest in option 3 i.e. " 12 payment of $ 550 beginning at the start of year 1 ".

Hope you understand the solution.