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An orcharder spends $105,000 to plant pomegranate bushes. It will take four years for the bushes...

An orcharder spends

$105,000

to plant pomegranate bushes. It will take four years for the bushes to provide a usable crop. He estimates that every year for 20 years after that he will receive a crop worth

$10,500

per year. If the discount rate is

9%​,

what is the net present value​ (NPV) of this​ investment?

A.

$11,129

B.

-$37,098

C.

−$18,549

D.

$ 7 420

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Answer #1

Solution: Correct option is B
Initial cash flow is -$105000 (negative sign shows it is a cash outflow)
It takes four years for the cash inflow to start. The sequence of cash flows are shown below:

CF0=-$105000
CF1=0
CF2=0
CF3=0
CF4=0
CF5=$10500 (Starting from CF5 the orcharder gets $10500 every year for 20 years)
CF6=$10500
CF7=$10500
CF8=$10500
CF9=$10500
CF10=$10500
CF11=$10500
CF12=$10500
CF13=$10500
CF14=$10500
CF15=$10500
CF16=$10500
CF17=$10500
CF18=$10500
CF19=$10500
CF20=$10500
CF21=$10500
CF22=$10500
CF23=$10500
CF24=$10500

Net present value is given by present value of cash outflows + present value of cash inflows

Here is how we will calculate the present value of cash inflows by using discount rate of 9%:

CF0=-$105000
CF1=0
CF2=0
CF3=0
CF4=0
CF5=$10500/(1+.09)^5=10500/1.5386=6824.28

CF6=$10500/(1+.09)^6=10500/1.6771=6260.81

CF7=$10500/(1+.09)^7=10500/1.8280=5743.86

CF8=$10500/(1+.09)^8=10500/1.99256=5269.60

CF9=$10500/(1+.09)^9= 10500/2.171893=4834.49

CF10=$10500/(1+.09)^10=10500/2.36736=4435.31

CF11=$10500/(1+.09)^11=10500/2.5804=4069.09

CF12=$10500/(1+.09)^12=10500/2.81266=3733.11

CF13=$10500/(1+.09)^13=10500/3.0658=3424.88

CF14=$10500/(1+.09)^14=10500/3.341727=3142.09

CF15=$10500/(1+.09)^15=10500/3.64248=2882.65

CF16=$10500/(1+.09)^16=10500/3.97030=2644.63

CF17=$10500/(1+.09)^17=10500/4.32763=2426.27

CF18=$10500/(1+.09)^18=10500/4.71712=2225.93

CF19=$10500/(1+.09)^19=10500/5.14166=2042.14

CF20=$10500/(1+.09)^20=10500/5.60441=1873.52

CF21=$10500/(1+.09)^21=10500/6.1088=1718.83

CF22=$10500/(1+.09)^22=10500/6.6586=1576.91

CF23=$10500/(1+.09)^23=10500/7.25787=1446.70

CF24=$10500/(1+.09)^24=10500/7.91108=1327.25

Present value of total cash inflows is equal to (0+0+0+0+6824.28+6260.81+5743.86+5269.60+4834.49+4435.31+4069.09+3733.11+3424.88+3142.09+2882.65+2644.63+2426.27+2225.93+2042.14+1873.52+1718.83+1576.91+1446.70+1327.25)
=$67902.36
Present value of total cash outflow is equal to -$105000
Therefore, NPV or net present value of this investment is equal to -$105000+$67902.36=-$37097.6 which is approximately equal to -$37098 as given in the option.

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