Question

You are an inventor and your firm has created a new agricultural technique of applying symbiotic fungus to seeds as they are planted and you patent this technique.

The benefits of your invention to the average farm, lasts for three years, and increases the profits of the farm by $7,000 at the end of the first year, $5,000 at the end of the second year, and $3,000 at the end of the third year. Farmers can borrow from their banks for agricultural inputs at a rate of 4.5%

In 1981, the Federal Reserve Chairman Paul Volcker raised the federal funds rate to 20% in an effort to combat inflation. The federal funds rate is a benchmark that other interest rates are compared to.

(Already Answered don’t need to Answer)** If suddenly the farmers could only borrow at 22.5%, what price will the symbiotic fungus application technique tend toward after the change in interest rates?

+10,678.21

(Already Answered don’t need to Answer)** Using the new price you just calculated, if the application technique still costs $5,000 to implment, what is your new NPV per application?

+5,678.21

(Please answer this and show steps)** If you still sell to 2,000 farmers per year, and you can now only borrow money at 24%, how much is your patent now worth?

(Please answer this and show steps)** Who benefits and who loses in this scenario when interest rates rise?

(Please answer this and show steps)** Calculate the percent change in the price of the application technique from the rise in interest rates.

(Please answer this and show steps)** Calculated the percent change in the value of your patent from the rise in interest rates.

(Please answer this and show steps)** If interest rate changes affect different members of society in such unequal ways, do you find interest rate control policies of the Federal Reserve to be just? Defend your answer.

Answer 1

A KL B C D E F G H The NPV table for the patent can be formulated using the given information as below: Period Benefit Discount rate Discount factor PV of benefit 1 3 0 7000 5000 3000 22.50% (New Fed rate should be used as the discount rate as given in the question) 1 0.816327 0.666389 0.543991 05714.286 3331.945 1631.9731 10678.2 PV of all benefits Using the given information, the NPV per patent application is given below PV of all future benefits 10678.2 Cost per application -5000 NPV of patent 5678.204 Since the discount rate has been changed to 24%, the new NPV table is given below Period Benefit Discount rate Discount factor PV of benefit PV of all benefits Cost per application NPV of patent 0 7000 5000 3000 24.00% (New Fed rate should be used as the discount rate as given in the question) 1 0.806452 0.650364 0.5244873 0 5645.161 3251.821 1573.4618 10470.44 -5000 5470.444 The pricing of the application technique is provided by the PV of all benefits which is $10,470.44 per application Since you can sell the patent to 2000 farmers per year, the total number of farmers in 3 years 6000

B C D E F G H I J K L M N And, the total value of the patent technique is now worth $ 62,822,665 Due to increase in interest rates, the price of the application technique has fallen by the difference in PV of future benefits per application ie Change in price = PV of future benefits (old) - PV of future benefits (new) 207.76 Thus, the inventor stands to lose $207.8 per application whereas the farmer stands to gain $207.8 per application due to the rise in interest rates % change in price of application technique from rise interest rates = Price of new technique - Price of old technique Price of old technique -0.01945643 -1.95 % % change in value of application technique from rise interest rates = NPV of new technique - NPV of old technique NPV of old technique -0.03658899 -3.66 % Interest rate control policies of Federal Reserve is predominantly driven by the inflation expecations in the economy A rise in interest rate is required to curb higher than comfort level of inflation growth Since the Federal Reserve in this case increased interest rates to combat inflation, the Fed is justified in its actions Although the effect of change in interest rates is different, Loss of 1.95% for inventor vs loss of 3.66% for farmer This can be justified using the fact that the inventor has the higher value share due its entrepreneurial action of improving benefits The farmer is a recipient of such an invention, thus the pricing control and hence the price effect is in the hands of inventor

Α G H The NPV table for the 0 3000 Period Benefit Discount rate Discount factor PV of benefit PV of all benefits 0.225 =1/(1+$D$5)-D3 =D6*D4 =SUM(D7:67) 2 7000 5000 (New Fed rate shoul =1/(1+$D$5)^E3 =1/(1+$D$5)^F3 =E6*E4 =F6*F4 =1/(1+$D$5) G3 =G6*G4 Using the given inforn PV of all future benefi Cost per application NPV of patent =D8 --5000 =E11+E12 Since the discount rati 3000 Period Benefit Discount rate Discount factor PV of benefit PV of all benefits Cost per application NPV of patent 7000 5000 (New Fed rate shoul =1/(1+$D$19)^E17 = 1/(1+$D$19)^F17 =E20*E18 =F20*F18 =1/(1+$D$19) G17 =G20*G18 0.24 =1/(1+$D$19)^D17 =D20*D18 =SUM(D21:421) -5000 =D22+D23 The pricing of the app Since you can sell the =2000*3

E F G H And, the total value of =B29*D22 Due to increase in inte per application ie Change in price = PV of future bene =D8-D22 Thus, the inventor sta due to the rise in inter % change in price of a Price of new technique - Price of old technique Price of old technique =(D22-D8)/D8 =1434100 % change in value of a NPV of new technique - NPV of old technique NPV of old technique =(D24-E13)/E13 =148*100 Interest rate control p A rise in interest rate i Since the Federal Rese Although the effect of Loss of 1.95% for inver This can be justified u The farmer is a recipie