Question

Draw a cash flow diagram and show ALL work for arriving at the final answer. I have given you the answers so that you will know if your answer is correct.

Two foresters are in disagreement concerning the proper grazing method for their uneven aged pine stand. Mr. X claims that by practicing continuous grazing he can receive an annual income of $800. The first income would be received at the end of the first year. Dr. Z claims that by practicing deferred grazing,she can receive an income of $2210 every three years, beginning at the end of the first year. If their opportunity cos tof capital (discount rate) is 4%, which method is more profitable, assuming grazing will occur for 28 years? (What is the present value of each grazing plan?) Answers (Mr. X: $13,330.45) (Dr. Z $13,241.21)

Answer 1

The present value of the benefit of Mr X = 800*(P/A,4%,28) = 800 * 16.663063 = 13330.45

The present value of the benefit of Mr Y = 2210*[(P/F,4%,1) + (P/F,4%,4) + (P/F,4%,7) + (P/F,4%,10) + (P/F,4%,13) + (P/F,4%,16) + (P/F,4%,19) + (P/F,4%,22) + (P/F,4%,25) + (P/F,4%,28) ]

= 2210*[0.961538 + 0.854804 + 0.759918 + 0.675564 + 0.600574 + 0.533908 + 0.474642 + 0.421955 + 0.375117 + 0.333477]

= 2210 * 5.99150

= 13241.208

= 13241.21

As PW of benefit of Mr .X is more, continuous grazing is better

CFD for Mr X

CFD for Mr. Y