Question

5.You own a plant producing oil. On 2017 the plant produced a quantity of 2,500 barrels of oil. The market price of a barrel of oil at 1.1.2018 is $50. Assume the plant's oil production is perpetual (lasts forever), all cash flows are received at the end of the year and the annual interest rate is 8%.

Calculate the plant's economic value at 1.1.2018 under the following scenarios. (The plant's value is equal to the present value of all the future cash flows it is expected to generate)

a.Oil production and the price of oil will remain constant at their present levels.

b.Oil production is constant, the price of oil increases at a rate of 3% per year.

c.Oil production increases at a rate of 9% each year, the price of oil remains constant.

7.The effective annual interest rate is 15%.

a.What is the effective interest rate for two years (accumulated over 2 years with interest over interest)?

b.What is the effective interest rate for ten years (accumulated over 10 years with interest over interest)?

c.Assume interest is compounded monthly. What is the monthly interest rate?

d.What is the simple annual interest rate?

e.What is the simple interest rate for 2 years? For 10 years?

8.

You deposit $175,000 in a savings account. The APR (Annual Percentage Rate) is 6%. Calculate the following:

a. Assuming that the interest is compounded once a year, what is the amount accumulated after ten years?

b. Assuming that the interest is compounded every month, what is the amount accumulated after ten years?

c. Assuming that the interest is compounded every day, what is the amount accumulated after ten years?

d. What is the observed effect of compounding at a higher frequency on the amount of money accumulated? Explain.

Answer 1

Since you have asked multiple questions and each question has sub parts, i am addressing all the sub parts of first two questions. Please post third question as a separate question on the Q&A board.

Question 5

Cash flow per annum, C₀ = Price of oil x Production quantity = $ 50 / barrel x 2,500 barrel = $ 125,000

Discount rate, K = annual interest rate = 8%

Economic Value = PV of all future cash flows = C₀ x (1 + g) / (K - g)

Please note that this formula is similar to Gordan growth model formula.

Part (a)

g = perpetual growth rate in the cash flows = 0% (Oil production and the price of oil will remain constant at their present levels.)

Hence, Economic value = = C₀ x (1 + g) / (K - g) = 125,000 x (1 + 0%) / (8% - 0%) = $ 1,562,500

Part (b)

Please note that the cash flows grow if either of its two constituents, that is price and quantity grow.

g = perpetual growth rate in the cash flows = 3% (Oil production is constant, the price of oil increases at a rate of 3% per year.)

Hence, Economic value = = C₀ x (1 + g) / (K - g) = 125,000 x (1 + 3%) / (8% - 3%) = $ 2,575,000

Part (c)

Please note that the cash flows grow if either of its two constituents, that is price and quantity grow.

g = perpetual growth rate in the cash flows = 9% (Oil production increases at a rate of 9% each year, the price of oil remains constant)

Since the growth rate, g = 9% > 8% = discount rate, the Gordan Growth model can't applied to calculate the value

Hence, Economic value is indeterminate in this case.

------------------------

7.The effective annual interest rate is 15%.

a.What is the effective interest rate for two years (accumulated over 2 years with interest over interest)?

Annual interest rate, i = 15%

If R₂ is the interest rate over 2 years then, (1 + R₂) = (1 + i)² = (1 + 15%)² = 1.3225

Hence, R₂ = 1.3225 - 1 = 0.3225 = 32.35%

b.What is the effective interest rate for ten years (accumulated over 10 years with interest over interest)?

Effective interest rate over 10 years, R₁₀ = (1 + i)¹⁰ - 1 = (1 + 15%)¹⁰ - 1 = 304.56%

c.Assume interest is compounded monthly. What is the monthly interest rate?

Let r be the monthly interest rate. Since it's compounded monthly the effective interest rate for the year = i = (1 + r)¹² - 1; hence 15% = (1 + r)¹² - 1

Hence, r = (1 + 15%)^(1/12) - 1 = 1.17%

d.What is the simple annual interest rate?

Simple annual interest rate = Effective annual interest rate = i = 15%

e.What is the simple interest rate for 2 years? For 10 years?

Simple interest rate for 2 years = 2 x i = 2 x 15% = 30%

Simple interest rate for 10 years = 10 x i = 10 x 15% = 150%