QUESTION 1

Your friend, Leah Nomvete, has just been employed as an economist. Fortunately, her father only last year gifted her with a car on her 22nd birthday, exactly eleven months ago. Ms. Nomvete currently lives with her parents in a neighborhood south of the city. Her target is to move to the northern suburbs in her own three-bed house on her 30th birthday. In the meantime, she plans to set aside an equal amount of money on a monthly basis to enable her to achieve this goal. Lately, she has been following property prices in the neighborhood of her interest very closely. Her boss, a renowned property investor, recently closed a deal on a property with design and features similar to what she has in mind just for ZAR 2,368,228 in that same neighborhood. Properties in the neighborhood have been appreciating at an average compound rate of 3% per year over the last several years. Property market analysts believe that this situation will prevail into the foreseeable future. Ms. Nomvete plans to save the same amount of money at the end of every month beginning the first month of her 23 birthday. She has identified a fund that currently pays interest at the rate of 6.5% per year, compounded monthly, on a savings plan.

i)How much money does Ms. Nomvete have to save each month to enable her to achieve the objective of owning her residential property at the end of her 30" birthday? (Assume that there are no brokerage commissions or legal fees on property purchase transactions), (4 marks)

Suppose Ms. Nomvete has decided that she will partially finance the purchase by borrowing a loan from a bank on the terms 80% loan-to-value ratio (LTV) on her 30 birthday. This means that the bank can extend a loan amounting to not more than 80% of the property's value. The interest rate on residential loans is expected to be 11% per annum with equal monthly instalment payments over 25 years. Further, Ms. Nomvete will have to pay legal costs amounting to 2% and bond fees amounting to 1% both based on the property value at the time of purchase. Since these costs cannot be borrowed, Ms. Nomvete must have adequate cash to pay for them separately. Her employer has promised to top up her savings by paying into the fund, on her 26 birthday, 30% of the amount accumulated as of that date. Under these circumstances, how much money does she have to set aside cach month to meet her objective? (5 marks)

ii) Compute Ms. Nomvete's expected monthly debt service. (Debt service is the total amount she is going to pay each month to cover both interest payments and principal repayments). The loan will be fully amortized. (2 marks)

Ms. Nomvete has decided that she must move out of her parents' residence on her 30th birthday whether or not she is buying her own property. She has two options available: buying or renting the property on her 30th birthday. At the moment, leases on properties of similar attributes as her "dream-house" are available at approximately ZAR 15,000 per month in the northern suburbs. Five years ago, leases on similar properties could be signed at about ZAR 12,000 per month. If she does not buy her own residence, she is going to sign a ten-year lease agreement with a landlord in the same suburb at the prevailing rentals; the rate of change in lease rentals is expected to remain constant over time. If she buys the property, she will finance the purchase partially using debt on the trms specified in part (b) above. She will live in it for ten years and then sell it at the market price. However, like other property-owners, she must pay property taxes amounting to ZAR 2750 every month to the local government. She must also pay service levies and property insurance of ZAR 2250 per month. Utilities and household insurance will cost her ZAR 1500 each month; however, she will also have to pay the same amount as a tenant under the leasing contract.

1. Estimate the rent payable on properties of the kind Ms. Nomvete is interested in when she is expected to sign the lease on her 30th birthday. Use the constant growth assumption (2 marks)
2. Compute Ms. Nomvete's monthly net cash flows (include opportunity costs and monthly debt service) if she buys the property on her 30th birthday. (3 marks)
3. 111) Compute her net proceeds from sale if she sells the property after ten years of occupation as she plans to. Ms. Nomvete expects to be in the 40% tax bracket for income taxation. Capital gains tax rate is 13.2%. Selling expenses average 4% of gross proceeds from property sales. (3 marks)
4. Compute Ms. Nomvete's net present value (NPV) from the property acquisition if she chooses the purchase option on her 30th birthday. Her required rate of return on investments of similar risk is 5.5% above the prime rate. The current prime rate is 10.75%; economic analysts are using a downward sloping yield curve (which can be estimated by a straight line with a slope of -0.05%). (6 marks)