Constant Growth Annuity

Constant Growth Annuity - Constant Growth Annuities Example...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Constant Growth Annuities Example 1: Cash Flow Starts at Year 0; Growth = 10%; Interest Rate = 5% Year CF: g = 10% PV: r = 5% 0 $100.00 $100.00 1 $110.00 $104.76 2 $121.00 $109.75 3 $133.10 $114.98 Present Value = $429.49 P 0 = $100*(1.10/1.05) 0 + $100*(1.10/1.05) 1 + $100*(1.10/1.05) 2 + $100*(1.10/1.05) 3 1.10/1.05 = 1.047619048 = 1.0476 (rounded off for this example only) Therefore, finding present value by growing a cash flow at 10 percent, then discounting it back at 5 percent, is the same as finding the present value by growing the cash flow at 4.7619048 percent. P 0 = $100*(1.0476) 0 + $100*(1.04786) 1 + $100*(1.0476) 2 + $100*(1.0476) 3 Even though we are finding the present value, MATHEMATICALLY, it looks like we are finding a future value of an annuity. What’s more, since we are compounding 1 of the annuity payments forward zero periods, MATHEMATICALLY, it looks like we are finding the future value as of the last payment (a regular annuity). Therefore, set your calculator to END of Period N = 4; I/YR = 4.7619048; PMT = 100; Solve for FV = $429.49 = Present Value ____________________ Example 2: Cash Flow Starts at Year 0; Growth = 5%; Interest Rate = 10% Year CF: g = 5% PV: r = 10% 0 $100.00 $100.00 1 $105.00 $95.45 2 $110.25 $91.12 3 $115.76 $86.97 Present Value = $373.54 P 0 = $100*(1.05/1.10) 0 + $100*(1.05/1.10) 1 + $100*(1.05/1.10) 2 + $100*(1.05/1.10) 3 Method 1 : 1.05/1.10 = (1/05/1.05) / (1.10/1.05) = 1 / 1.047619048 = 1 / 1.0476 (rounded off for this example only)
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Therefore, finding present value by growing a cash flow at 5 percent, then discounting it back at 10 percent, is the same as finding the present value by discounting the cash flow at 4.7619048 percent. P 0 = $100 / (1.0476) 0 + $100 / (1.04786) 1 + $100 / (1.0476) 2 + $100 / (1.0476) 3 This looks like we are finding the present value as of the first payment (an annuity due). Therefore, set your calculator to BEGIN of Period
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/11/2011 for the course FIN 3403 taught by Professor Tapley during the Spring '06 term at University of Florida.

Page1 / 6

Constant Growth Annuity - Constant Growth Annuities Example...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online