Question

The city of Ashkelon, on the eastern end of the Mediterranean Sea, is one of the major cities of the Philistines. A powerful merchant family (known henceforth as The Family) of this city has to decide how to allocate its vast but finite resources to further their own wealth and the glory and influence of their state. Some trade routes use camel caravans and go to the southern deserts, where they may trade in salt and gold with the great inland African nations; others may go north and west, oversea by galley, toward the Greeks; others may push their foul-mouthed, humped mounts east, overland toward Sumeria, to trade in spices and the crafted goods specific to that region. Some of the routes are over more arduous terrain than others, so make take longer to pay off (no revenue is realized by The Family until the caravan returns to Ashkelon). The financial costs and returns of each route are as follows (in Phils, the currency of the Philistines):

Route Costs, Period 0 Revenue, Period1 Revenue, Period 2 Revenue, Period 3
African Route -75,000 215,000
Greek Route -50,000 140,000
Sumerian Route -125,000 385,000

Costs are incurred at the end of year zero, and revenues accrue at the end of Periods 1, 2, and 3, for each respective route (for instance, the African caravan returns at the end of period two, at which time its revenue is realized). The discount rate for the shipping company is 5%.

Required:
a. Calculate the NPV, B/C ratio, Payback period, and IRR for each route option.
b. Rank the route options according to NPV, B/C ratio, Payback period, and IRR.
c. If the company had unlimited funds, which trade routes would you recommend the family pursue? Why? Be sure to consider all combinations of routes, including multiple caravans on the same trade route.
d. Given that the family can only invest 150,000 Phils, which combination of trade routes would you recommend pursuing? Why?

Answer 1

African Route costs = -75,000, period 1 revenues = 215,000

Greek Route costs = -50,000, period 2 revenues = 140,000

Sumerian Route costs = -125,000, period 3 revenues = 385,000

discount rate = 5%

a) African route:

NPV = -75,000 + 215,000/1.05 = 129,762

B/C ratio = 215/75 = 2.87

Payback = 1 period

IRR = 187%

Greek route:

NPV = -50,000 + 140,000/1.05² = 76,984

B/C ratio = 140/50 = 2.8

Payback = 2 periods

IRR = 67%

Sumerian route

NPV = -125,000 + 385,000/1.05³ = 332,577

B/C ratio = 385/125 = 3.08

Payback = 3 periods

IRR = 45%

b) rank according to:

NPV = Sumerian route, African route, Greek route

B/C ratio = Sumerian route, African route, Greek route

Payback = African route, Greek route, Sumerian route

IRR = African route, Greek route, Sumerian route

c) if the family had unlimited resources, they should invest in the 3 routes since all their NPVs are positive.

d) African and Greek routes since they yield the highest gains (IRR).