4. Jerry intends to use the money from his loan (and his personal savings if necessary) to make an investment in his friend Elaine’s business. In return, Elaine has predicted the following returns on Jerry’s investment: • Four half-yearly payments of $10,000, the first being exactly 6 months from today, • Four half-yearly payments of $20,000, the first being exactly 6 months after the final $10,000 payment described above, and • Two half-yearly payments of $25,000, the first being exactly 6 months after the final $20,000 payment described above (i.e. there are 10 half-yearly payments in total, the final one occurring exactly 5 years from today). Whilst Elaine is a trusted friend and a capable businesswoman, Jerry has some doubts. To make a more conservative assessment of the investment, Jerry will expect a higher rate of return. Jerry decides that he requires the following return on his investment: • 12% p.a. effective for the first 2 years of the investment, and • 15% p.a. compounding quarterly for the remaining term of the investment. Using this information, answer the following questions. e) For the two rates given above, determine the equivalent effective half-yearly rates. Clearly label your answers. f) Using your results from part e), draw a cash flow diagram, and then determine the maximum price Jerry would be willing to pay for this investment. g) Jerry makes an offer to Elaine of the price calculated in part f). Elaine thinks for a moment, and gives a counter-offer of $115,000. Write down an equation that can be solved to determine Jerry’s return on his investment using Elaine’s new price, expressed as an effective half-yearly rate. You do NOT need to solve this equation
4. Jerry intends to use the money from his loan (and his personal savings if necessary) to make an investment in his friend Elaine’s business. In return, Elaine has predicted the following returns on Jerry’s investment:
• Four half-yearly payments of $10,000, the first being exactly 6 months from today,
• Four half-yearly payments of $20,000, the first being exactly 6 months after the final $10,000 payment described above, and
• Two half-yearly payments of $25,000, the first being exactly 6 months after the final $20,000 payment described above
(i.e. there are 10 half-yearly payments in total, the final one occurring exactly 5 years from today). Whilst Elaine is a trusted friend and a capable businesswoman, Jerry has some doubts.
To make a more conservative assessment of the investment, Jerry will expect a higher rate of return. Jerry decides that he requires the following return on his investment:
• 12% p.a. effective for the first 2 years of the investment, and
• 15% p.a. compounding quarterly for the remaining term of the investment.
Using this information, answer the following questions.
e) For the two rates given above, determine the equivalent effective half-yearly rates. Clearly label your answers.
f) Using your results from part e), draw a cash flow diagram, and then determine the maximum price Jerry would be willing to pay for this investment.
g) Jerry makes an offer to Elaine of the price calculated in part f). Elaine thinks for a moment, and gives a counter-offer of $115,000. Write down an equation that can be solved to determine Jerry’s return on his investment using Elaine’s new price, expressed as an effective half-yearly rate. You do NOT need to solve this equation
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