Question

15. The price at harvest is $4.50. You are planning to store for 5 months. The amount to be stored is 40,000 units. The insurance per unit is estimated at $.05 per unit. The spoilage loss rate is 3%. The interest rate is 5%. Your forecast is that if you store, the market price will be $5.50 in 5 months. Should you store or sell now? (15 pts) Price at Harvest (Ph) $4.50 40,000 units Amount at Harvest (Qh) Revenues if Sold at Harvest (Ph*Qh) Price if Store (Ps) $5.50 $/unit Units Spoilage Loss Amount (SL) Amount after Store (Qs-SL) Units Revenues after Storage, With Storage Loss Rs=Ps*(Qs-SL) Insurance Costs (INS) Revenues After Storage and Insurance Costs (Use as Future Value, FV) FVERS-INS Annual Interest Rate (1) Monthly Interest Rate (MI=1/12) Discounted Value DV=FV/(1+MI)" n=number of time periods stored Store (Yes or No) % in Decimal % in Decimal S Yes/No Show DV Calculations Here: DV=FV/(1+MI)" =

Answer 1

SOLUTION:-

Price at harvest (Ph): $4.50

Amount at Harvest (Qh): 40,000 units

Revenues if sold at harvest (Ph*Qh): 4.5 * 40000 = $180,000

Price if store (Ps): $5.50 / unit

Spoilage Loss Amount (SL): 40,000 * 3% (spoilage rate is 3%) = 1,200 units

Amount after Store (Qh - SL): 40000 - 1200 = 38,800 units

Revenues after storage with storage loss (Rs = Ps*(Qh-SL)): $5.50 * 38,800 = $213,400

Insurance Costs (INS) = $ 0.05 per unit * 40,000 = $2,000

Revenues after Storage and Insurance costs (Use as Future value, FV) FV = Rs - INS = 213,400 - 2000 = $211,400

Annual Interest Rate (I): 5.00%

Monthly Interest Rate (MI = I/12): 5.00 /12 = 0.4167%

Discounted Value DV = FV / (1 + MI)ⁿ ; n = number of time periods stored = (5 yrs*12 mts = 60):    $211,400 / (1+0.004167)⁶⁰ = $164,720

Store (Yes / No): No (since the sale at present yields higher revenue than the present value of the storage decision)

DV calculations:

DV = FV / (1 + MI)ⁿ

= $211,400 / (1+0.004167)⁶⁰

= $211,400 / 1.004167⁶⁰

= $211,400 / 1.283384 ….(use PV table if provided or use calculator; Type 1.004167, press x sign twice so k appears on screen, then press = while counting 2, press again & count 3 and so on till count 60 is reached)

= $164,720