Question

A farmer estimates that a 50 acre peach orchard will require an initial investment of $25,000 for soil preparation and tree purchase and planting costs. Assume the farmer already owns the land that the orchard will be planted on. After planting, cash outflows are expected in years 1-3 as the young trees are established and produce no harvestable crops. Assume outflows of $10,000, $5000, and $5000 in years 1 through 3, respectively. In years 4 and 5 production will occur at one half and three quarters of full production, respectively, so revenues will pay a portion of expenses, and cash outflows of $1000 in year 4 and inflows of $2000 in year 5 will be incurred. In years 6-20, the orchard will be at full production and the annual net cash inflows are projected to be $5000. After 20 years of useful life, the potential of reduced yields and the development of new varieties usually make it necessary to consider the replacement of an orchard. So assume that the orchard will be replaced after year 20 and that there is no salvage value at that time. Assume the farmer has a cost of capital of 9%. What is the approximate net present value of the orchard? HINT: DRAW A TIMELINE OF CASH INFLOWS AND OUTFLOWS

		$32,530
		-$9,620
		$13,780
		-$15,460

Answer 1

Option D is the correct answer

H K NPV PV @ 9%| Present Value Year Cash Flow $ -25,000.00 0.9174 $ -9,174.00 $-25,000.00 1 1$-10,000.00 2 $-5,000.00 3 $-5,000.00 4 $-1,000.00 5$ 2,000.00 6 $ 5,000.00 0.8417 S -4,208.50 0.7722 $3,861.00 0.7084 $ -708.40 0.6499 $ 1,299.80 0.5962 S 2,981.00 7 $ 5,000.00 8 $ 9 $ 5,000.00 10$ 5,000.00 11 $ 5,000.00 12 $ 5,000.00 13 $ 5,000.00 14 $5,000.00 15 $ 5,000.00 0.547 $ 2,735.00 0.5018 S 5,000.00 2,509.00 0.4604 S 2,302.00 0.4224 $ 2,112.00 0.3875 $ 1,937.50 0.3555 $ 1,777.50 0.3261 $ 1,630.50 0.2992 $ 0.2745 $ 1,496.00 1,372.50 16 $ 5,000.00 17 $ 5,000.00 $5,000.00 19 $ 5,000.00 20 $ 5,000.00 0.2518 $ 1,259.00 0.231 $ 1,155.00 0.2119 $ 1,059.50 0.1944 $ 972.00 0.1783 $ 891.50 $ NPV -15,462

J 1 NPV Cash Flow Present Value 2 Year PV 9% 3 0 -25000 1 - 13* J3 =ROUND (J3 /1.09,4)14*J4 -ROUND (J4 / 1.09,4)15J5 =ROUND (J5/1.09,4)16*J6 =ROUND(J6/1.09,4) 17*J7 =ROUND(J7/1.09,4)18J8 =ROUND(J8/1.09,4)19*9 =ROUND (J9/1.09,4)10*J10 =ROUND(J10/1.09,4 11*J11 -ROUND (J11 /1 .09,4 112*J12 =ROUND(J12/1.09,4-113*J13 -ROUND (J13 /1 .09,4114*J14 =ROUND(J14/1.09,4=115*J15 |=ROUND(J15/1.09,4116*J16 =ROUND (J16/1.09,4-117*J17 -ROUND (J17 /1.09,4 118*J18 =ROUND (J18/1.09,4-119*J19 -ROUND (J19 /1 .09,4 120*J20 =ROUND (J20/1.09,4=121 J21 =ROUND (J21 /1.09,4 122J22 =ROUND (J22/1.09,4-123*J23 -SUM(K3:K23) 4 1 -10000 5 H4+1 -5000 6 H5+1 -5000 7 - H6+ 1 -1000 H7+1 2000 8 5000 9 -H8+ 1 10 H9+1 5000 11H10+1 5000 12H11+1 5000 13 H12+1 5000 14 H13+1 5000 15 H14+1 5000 16H15+1 5000 17 H16+1 5000 18H17+1 5000 19H18+1 5000 20 H19+1 5000 21 H20+1 5000 22 H21+1 5000 23 H22+1 5000 24 NPV 25 I