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You want to buy a house using a 15-year fixed-rate mortgage from the bank. Given your income, you are willing to pay up to $3,000 per month in monthly mortgage payments and want to borrow 70% of the house price from the bank. You have sufficient cash in your bank account to pay the remaining 30% of the house price. The monthly payments will start one month after receiving the loan and the interest rate is 4.8% per annum compounding monthly.
(a) What is the highest price that you can pay for a house?
(b) Assuming that you bought a house for the highest possible price, what is the principal left on your mortgage after 5 years?
Consider a ten-year, $100 bond with an 8% coupon rate and a price of $103.64.
(a) What is the YTM if the bond made annual coupon payments?
(b) What is the YTM if the bond made semi-annual coupon payments?
(c) What is the YTM if the bond made quarterly coupon payments?
The government wants to encourage homeownership and has enacted a program that will supply low-income households with housing that is 50% the price of comparable houses. You are eligible to buy a house under this program and want to know how good this investment is in comparison to other possible investments. If you decide to participate, you will need to pay $50,000 immediately, $100,000 in 1 year, and $350,000 in two years when the house will be fully built and will be ready to be occupied. However, the government is concerned that low-income households may have trouble paying for the payment amount in year 2 and will provide a 30-year fixed-rate mortgage for the $350,000 payment in year 2. You plan on making full use of this government-provided mortgage and will not take on other debt. This mortgage will have annual payments at an interest rate of 1.2% per annum. The annual mortgage payments will start one year from receiving the loan. Because you are looking to buy this house for investment purposes, you will rent it out instead of living in it. If you buy this house, you will rent it to a potential tenant who will give you a large deposit in exchange for a reduction in the rent. The tenant will pay a $150,000 deposit when moving into the house 2 years from now and will pay an annual rent of $10,000 at the end of the first year of living in the house. The tenant will pay annual rent at the end of each following year, where the rent will increase by 2% each year. The deposit will not change. 10 years after the house is built, the tenant will move out and you will need to return the deposit to the tenant. The price of comparable houses now is $1,000,000 and you expect housing prices to increase by 2% each year. You plan to sell the house 10 years after it is built at the expected market price. When you sell your house, you will need to repay the remaining principal on the mortgage. Ignore taxes. If your discount rate is 10% per annum, what is your IRR on this investment?