(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 not profit. Did you forget something – like the cost of 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).
to calculate NPV we need initail investment,discount rate and CF projections.
the time duration of the project is 3 years and generates positive CF occurs after 9 months
so initial investment=cost of buying shrimps+cost of equipment of keeping shrimp
= $[(20*3)+200]
= $260
to calculate CF we are given that it will take 9 months to start selling the shrimp while the monthly shrimp food expense will still be incurred
So,CF from month 1 to month 9= -$6
CF from month 10 to 36=(profit from selling 5 shrimps - cost of food)
=(5*3) - 6
=$9
at the end of 3 years given 100 shrimps are sold at once= 100*3
= $300
so CF on the 36th month=300+9
=$309
no using financial calculator;
enter CF mode
CF0=+/-260
CF1=+/-6 AND F01=9(this is the frequency i.e 9 months)
CF2=9 AND F02=26(Excluding the 36th month)
CF3=309
ENTER NPV
I=0.25 THEN CPT=190.36
HENCE THE NPV OF KEEPING THE SHRIMP PROJECT IS 190.36.
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