Question

(Based on a true story. No fish or shrimp is harmed during the production of this question.)

Cast of Characters

Dr. H:               A college professor of Finance in a Private University. He believes the true path towards happiness is through studying Finance.

Wife of Dr. H (WIFE):     A former college accounting major who currently works as the VP of Finance in a local tech company.

Time

The present.

SETTING:         Living room at the house of Dr. H and his wife.

AT RISE:           Dr. H’s wife is seated at her working desk. The door opens and Dr. H enters the room.

Dr. H:               I am home! And guess what? I bought shrimps.

WIFE:               I was planning to cook lamb chops for dinner, but I guess we can have some seafood for a change. How much did you pay for them?

Dr. H:               3 dollars.

WIFE:               Per pound?

Dr. H:               Per shrimp.

WIFE:               What? Then they better be of a good size, a VERY good size.

Dr. H:               They are between half inches to 1 inch. Look, these are not for food. These are live shrimps for my aquarium, you know, my 20-gallon fish tank.

WIFE:               But paying 3 dollars for these tiny creatures is ridiculous. How many did you buy?

Dr. H:               Twenty. Listen, these shrimps are going to bring me so much fun and joy. Plus, it could be a sound financial investment.

WIFE:               Financial investment? What are you talking about?

Dr. H:               Look, these cherry red shrimps not only look good, but they breed easily. In no time, I am gonna have juvenile shrimps of my own that I can then sell for profit.

WIFE:               How long until that happens?

Dr. H:               Well, I need to first grow my 20 shrimps to a stable large population before I can sell some. It will take probably 9 months.

WIFE:               After that, how many can you sell each month?

Dr. H:               Around 5.

WIFE:               At 3 dollars each?

Dr. H:               Correct. See? That’s 15 dollar profit right there.

WIFE:               Need I remind you that I was an accounting major in college? That’s notprofit. Did you forget something – like the costof keeping them?

Dr. H:               Uh, you are right, my bad. I will need to spend another 200 dollars on equipment now. Then each month probably need to spend 6 bucks on shrimp food.

WIFE:               If you sell 5 shrimps every month, will that deplete your population over time?  

Dr. H:               Negative. The natural growth of the shrimp population allows me to do this in a sustainable manner.

WIFE:               How long do you plan to keep these shrimps?

Dr. H:               I don’t know. Let’s say 3 years. At the end, I will probably have around 100 shrimps that I can sell all at once and keep some other creatures in that tank.

WIFE:               This starts to sound attractive now. You know what? All these talks about the shrimp make me crave for some seafood. Forget about lamb chops. Want to continue this discussion at Red Lobster?

Dr. H:               Great idea. You call to make a reservation and I will grab the car key.

END OF THE SCENE

With a monthly discount rate of 0.25%, help Dr. H’s wife find out the NPV of this shrimp keeping project(include the cash Dr. H just spent on the shrimp as a relevant cash flow, i.e. don’t treat that as sunk cost).

Answer 1

Initial investment = 20 Shrimps * 3 dollars each = $60

Plus: equipment = $200

Therefore, total initial investment = 60+200 = $260

From the above, it can be seen that,
For 9 months from today, we will not have any revenue. Only expenses.

Income will start getting generated from month 10. Assuming 5 shrimps per month @ $3 per shrimp = $15 per month of revenue for the next 3 years, including the 9 months in the beginning. $6 / month of expenses. Therefore, $15-$6 = $9 per month profit can be taken.

At the end of the 3 years, cash inflow would be 100*$3 = $300, and the project ends.

Using Excel, we can map out the calculation as below. Assume the top-left cell to be cell A14

Month	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30	31	32	33	34	35	36
Profit											9	9	9	9	9	9	9	9	9	9	9	9	9	9	9	9	9	9	9	9	9	9	9	9	9	9	300
Discount Factor	=1/(1+0.25%)^B14	=1/(1+0.25%)^C14	=1/(1+0.25%)^D14	=1/(1+0.25%)^E14	=1/(1+0.25%)^F14	=1/(1+0.25%)^G14	=1/(1+0.25%)^H14	=1/(1+0.25%)^I14	=1/(1+0.25%)^J14	=1/(1+0.25%)^K14	=1/(1+0.25%)^L14	=1/(1+0.25%)^M14	=1/(1+0.25%)^N14	=1/(1+0.25%)^O14	=1/(1+0.25%)^P14	=1/(1+0.25%)^Q14	=1/(1+0.25%)^R14	=1/(1+0.25%)^S14	=1/(1+0.25%)^T14	=1/(1+0.25%)^U14	=1/(1+0.25%)^V14	=1/(1+0.25%)^W14	=1/(1+0.25%)^X14	=1/(1+0.25%)^Y14	=1/(1+0.25%)^Z14	=1/(1+0.25%)^AA14	=1/(1+0.25%)^AB14	=1/(1+0.25%)^AC14	=1/(1+0.25%)^AD14	=1/(1+0.25%)^AE14	=1/(1+0.25%)^AF14	=1/(1+0.25%)^AG14	=1/(1+0.25%)^AH14	=1/(1+0.25%)^AI14	=1/(1+0.25%)^AJ14	=1/(1+0.25%)^AK14	=1/(1+0.25%)^AL14
PV	=SUMPRODUCT(B15:AL15,B16:AL16)
Investment	=260
NPV	=B18-B19

Actual Values are shown below:

Month	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30	31	32	33	34	35	36
Profit											9	9	9	9	9	9	9	9	9	9	9	9	9	9	9	9	9	9	9	9	9	9	9	9	9	9	300
Discount Factor	1.0000	0.9975	0.9950	0.9925	0.9901	0.9876	0.9851	0.9827	0.9802	0.9778	0.9753	0.9729	0.9705	0.9681	0.9656	0.9632	0.9608	0.9584	0.9561	0.9537	0.9513	0.9489	0.9466	0.9442	0.9418	0.9395	0.9371	0.9348	0.9325	0.9301	0.9278	0.9255	0.9232	0.9209	0.9186	0.9163	0.9140
PV	495.47
Investment	260
NPV	235.47