Question

Eight12 is a large chain of convenience stores, with a number of outlets throughout Europe. The stores are conveniently located at street corners or other busy parts of urban centers and carry a limited selection of everyday items such as fruits, bread and pastries, snacks, tobacco products and magazines.

The last mile distribution network for Eight12's stores in Berlin, Germany, is designed like many other last mile distribution networks. Just outside the city, Eight12 has a distribution center (DC). From this DC, a large fleet of company-owned and operated trucks supply the stores in and around Berlin. Most stores are replenished daily from the DC.

Recently, Eight12 decided to completely redesign their last mile distribution network in Berlin. The company's idea was to completely rethink their whole network design, including how many stocking points and cross-docking points to have in the city, as well as how many vehicles, and of which type, to operate within the network.

The supply chain analytics team at Eight12 was given the task of coming up with alternative designs for this revised network. After six months of meetings, discussions, number crunching, and a well-received off-site conference at a ski resort in the Swiss mountains, the team has decided to propose two alternative designs to the VP of Supply Chain, as follows:

• Alternative 1 is a mobile multi-tier network. With this design, Eight12 will need to invest in mobile stocking points, as well as smaller electric distribution vehicles. The mobile stocking points are basically large trucks that will act as temporary stocking locations from which the smaller distribution vehicles distribute to each store. This solution will provide a lot of flexibility and reduce fuel costs for Eight12. However, this design is conceptually and operationally very different from the current distribution network.
• Alternative 2 is a more traditional network. This alternative consists of updating the fleet of trucks and retaining the current DC. The company would invest heavily in the current DC, in order to make it efficient and capable of supporting future growth.

Both alternatives are assumed to pay back within 2 years. The alternatives are mutually exclusive.

Part 1

The aggregated cash flows, in dollars, for each of the two alternatives are given in the table below.

Relative Cash Flows compared to current operations for year 0 and the first two years

	Year 0	Year 1	Year 2
Alternative 1	-804980	+365900	+731800
Alternative 2	-852547	+731800	+365900

Eight12 is currently using a discount rate of 10% to evaluate all proposed projects.

What is the internal rate of return (IRR) for each of the two alternatives?

IRR for Alternative 1:

IRR for Alternative 2:

Part 2

What is the net present value (NPV) for each of the two alternatives? Remember that Eight12 is currently using a discount rate of 10% to evaluate all proposed projects.

NPV for Alternative 1

NPV for Alternative 2

If the discount rate was 25%, what alternative should the firm choose?

Alternative 1 or Alternative 2 or neither?

Answer 1

IRR is the rate of return at which NPV becomes zero.

we will first calculate NPV AT 10% for both alternatives.

Alternative 1

	Cash flow	Discount factor at 10%	Present value of cash flows
Year 0	(804980)	1	(804980)
1	365900	0.9091[1/1.10]1	332640[365900*0.9091]
2	731800	0.8264[1/1.10]2	604760[731800*0.8264]
		NPV	132420 $
		cash inflow-cash outflow	[332640+604760-804980]

Alternative 2

	Cash flow	Discount factor at 10%	Present value of cash flows
Year 0	(852547)	1	(852547)
1	731800	0.9091[1/1.10]1	665279[731800*0.9091]
2	365900	0.8264[1/1.10]2	302380[365900*0.8264]
		NPV	115112 $
		cash inflow-cash outflow	[665279+302380-852547]

Both the alternative have positive NPV HOWEVER THEY ARE mutually exclusive so only one out of two should be selected.

The firm should choose alternative 1 as it has a higher NPV THAN alternative 2 at discount rate of 10%

DISCOUNT RATE 25%

Alternative 1

	Cash flow	Discount factor at 25%	Present value of cash flows
Year 0	(804980)	1	(804980)
1	365900	0.8[1/1.25]1	292720[365900*0.80]
2	731800	0.64[1/1.25]2	468352[731800*0.64]
		NPV	43908 $
		cash inflow-cash outflow	[292720+468352-804980]

Alternative 2

	Cash flow	Discount factor at 10%	Present value of cash flows
Year 0	(852547)	1	(852547)
1	731800	0.80[1/1.10]1	585440[731800*0.80]
2	365900	0.64[1/1.10]2	234176[365900*0.64]
		NPV	32931 $
		cash inflow-cash outflow	[665279+302380-852547]

Both the alternative have positive NPV HOWEVER THEY ARE mutually exclusive so only one out of two should be selected.

The firm should choose alternative 1 as it has a higher NPV THAN alternative 2 at discount rate of 25%

IRR ALTERNATIVE 1

we will use NPV OF 10% AND 25% TO DERIVE AT IRR

R1 = 10% 0.10

R2 = 25% 0.25

NPV1 =132420

NPV 2 =43908

R1 +[NPV1 * (R2-R1)/(NPV1-NPV2)]

0.10 + [132420 * (0.25-0.10) / (132420-43908)]

0.10 + [19863/88512]

=0.10+0.2244

=0.3244

=32.44%

32.44% NPV WOULD BE ZERO.

SO IRRFOR ALTERNATIVE = 32.44%

ALTERNATIVE 2

R1 = 10% 0.10

R2 = 25% 0.25

NPV1 =115112

NPV 2 =32931

R1 +[NPV1 * (R2-R1)/(NPV1-NPV2)]

=0.10 + [(115112 * (0.25-0.10)] / [115112-32931]

=0.10 + 17267/82181

=0.10+0.21010

IRR FOR ALTERNATIVE 2=31.01%