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Bonita intends to open a small fabric shop and borrows the money for it from her aunt Magda. Bonita feels that she will only be able to start repaying her debt after three years. Bonita will then pay aunt Magda R105 000 per year for five years. Money is worth 19,5% per year. The amount of money that aunt Magda originally lent Bonita is
Frieda will discharge a debt of R500 000 six years from now, using the sinking fund method. The interest of the debt is 15,6% per year, paid quarterly. The sinking fund earns interest at a rate of 8,4% per year, compounded monthly. The total yearly cost to discharge the debt (to the nearest rand) is
Marang borrowed money that must be repaid in nine payments. The first four payments of R2 000 each are paid at the beginning of each year. Thereafter five payments of R5 000 each are paid at the end of each year. Note there is only one payment per year. If money is worth 6,85% per year, then the present value of these payments is
Thulisile bought a house and managed to secure a home loan for R790 000 with monthly payments of R9 680,70 at a fixed interest rate of 13,75% per year, compounded monthly, over a period of 20 years. If an average yearly inflation rate of 9,2% is expected, then the real cost of the loan (the difference between the total value of the loan and the actual principal borrowed) is
You are saving to pay for your children’s university costs in 20 years’ time. In the first year, your payment is R3 600, after which your yearly payments increased by R360 each year. If the expected interest rate per year is 10%, the amount that you expect to receive to the nearest rand on the maturity date will be
After an accident Nomfundo was awarded an amount from the Road Accident Fund as compensation for her injuries. She chose to receive R18 900 per month indefinitely. If money is worth 9,95% per year, compounded monthly, then the amount awarded is approximately
Moshe will need R145 000 in three years’ time, to open a bakery. He immediately starts to make monthly deposits into an account earning 11,05% interest per year, compounded monthly. Moshe’s monthly deposit is
An amount of R600 is invested every month for eight years. The applicable interest rate is 14,65% per year, compounded quarterly. The accumulated amount of these monthly payments is approximately
Kusho Industries produces and sells computer chips. Its (hourly) production function is 𝒒 = 𝟒𝑲𝟎.𝟒𝑳𝟎.𝟔, while its (hourly) cost function is 𝒄 = 𝟐𝟎𝑳 + 𝟖𝟎𝑲. Furthermore, Kusho must produce 𝒒𝟎 = 𝟒𝟎𝟎 computer chips per hour.
a. Which levels of 𝑳 and 𝑲 satisfy the first-order conditions for the constrained minimisation of Kusho’s
cost? Use the Lagrange Multiplier (LM) method. Also, find and interpret the value of the Lagrange
multiplier (𝝀). [8]
b. Show that 𝑴𝑹𝑻𝑺 = 𝒘 at the constrained cost minimising levels of 𝑳 and 𝑲 obtained above. [2]
Suppose you are evaluating two mutually exclusive projects, Thing 3 and Thing 4, with the following cash flows:
Thing 3 Thing 4 2000 −$10,000 −$10,000 2001 3,503 0 2002 3,503 0 2003 3,503 0 2004 3,503 19,388 End-of-year cash flows Year
(a)
If the cost of capital on both projects is 5%, which project, ifany, would you choose? Why?
(b)
If the cost of capital on both projects is 10%, which project, ifany, would you choose? Why?
(c)
If the cost of capital on both projects is 15%, which project, ifany, would you choose? Why?
(d)
If the cost of capital on both projects is 20%, which project, ifany, would you choose? Why?
(e)
At what discount rate would you be indifferent between choosing Thing 3 and Thing 4?
(f)
On the same graph, draw the investment profiles of Thing 3 and Thing 4. Indicate the following items:
•
cross-over discount rate
•
NPV of Thing 3 if the cost of capital is 10%
•
NPV of Thing 4 if the cost of capital is 10%
#340153 on Dec 2023