An agricultural produce company located in Iowa can deliver up to 2,000, 000 fre

Question

An agricultural produce company located in Iowa can deliver up to 2,000, 000 fresh greens units per year. The demand in Year 1 is 1,000,000 units in state, and 500,000 units out of state. The out of state demands need to be shipped to the demand locations, while no shipping (ei- ther by truck or by a third party company) is required in-state. The selling price per unit is $2.5, while the production costs $1 per unit. Finally, the company uses a discount factor k 0.1 For shipping, there are two options 1. Use a shipping company, which costs $50,000 per year. Then, produce can be shipped with a cost of $0.25 per unit. As noted before, you do not pay shipping costs for deliveries n lowa. 2. Lease trucks as needed with a cost of $7,500 per truck. Each truck can carry up to 20,000 units. No other shipping costs are incurred. As noted earlier, you do not need to lease trucks to deliver in Iowa Market research has revealed that demand in Iowa is equally likely to either increase to 1,500,000 units or stay the same in the next year (Year 2). Demand out of state is expected to stay the same (that is at 500.000 units) during that time. In the year after that (Year 3) there is a 25% probability that in-state demand increases by 50% and a 75% chance that it stays the same. For out-of-state demand, there is a 40% chance it increases by 50% and a 60% chance that it increases by 100% (doubles from Year 2) (a) Draw the decision tree (b) What is the NPV of using a shipping company? (c) What is the NPV of leasing trucks as needed? Answer

Explanation / Answer

Solution (a) Year 1 Year 2 Year 3 No. of units With in State 1000000 1250000 1125000 WN-1 WN-2 out of state 500000 500000 875000 WN-2 Total 1500000 1750000 2000000 SP 2.5/- Production cost 1/- Cont. per unit 1.5/- Solution (b) Year 1 Year 2 Year 3 Cont/- 2250000 2625000 3000000 less Shipping cost 125000 125000 218750 (0.25*500000) (0.25*500000) (0.25*875000) Profit 2125000 2500000 2781250 Calculation of NPV,k=10% (2125000*0.909)+(2500000*0.826)+(2781250*0.751) 6085343.75 i.e 6085344/- Solution (c) Year 1 Year 2 Year 3 Cont/- 2250000 2625000 3000000 Less: leasing cost 187500 187500 330000 (no of trucks*7500) (25*7500) (25*7500) (44*7500) no of trucks 25 25 43.75 (total demand/capacity per truck i.e 20000) (500000/20000) (500000/20000) (875000/20000) Profit 2062500 2437500 2670000 Calculation of NPV,k=10% (2062500*0.909)+(2437500*0.826)+(2670000*0.751) 5893357.5 i.e 5893358/- Working note: WN-1 Calculation of Demand(yr 2) With in state (1500000*50%)+1000000*50% 1250000 Taking probability equal for 1500000/- and 1000000/- units of sale i.e P=50% WN-2 Calculation of Demand (yr 3) with in state demand=1500000(1000000+1000000*50%),p=25% Demand=1000000,p=75% (1500000*25%)+1000000*75% 1125000 out of state demand=750000(500000+500000*50%),p=40% Demand=1000000(500000*100%+500000),p=60% (750000*40%)+1000000*60% 900000 but demand of 875000 could be meet only as maximum capacity of production is 2000000/- units per year. we don't meet out of state demand fully due to shipping cost involved consequently profit contribution is low as compare to local units.

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