Question

12) Roy owns an investment property that is net leased to a tenant that pays rent in advance. If annual rent is $6,000 and increases 2% per annum, how much is the investment worth assuming a 6-year holding period and 13% discount rate? 13) Jan paid $20,000 for an investment that now generates $1,500 each year in income. Assuming a 5-year holding period, what is the discount rate? 14) Toby paid $50,000 for an investment property that yields $5,000 per annum with 2% per annum increases. Assuming a 7-year holding period and $130,000 reversion, what is the IRR? If a typical market participant would receive a 12% return on periodic cash flows, what would the adjusted rate of return be on this investment? 15) Kelly bas a $65,000 loan for a 30 -year term with 11% interest with monthly payments. How much are her monthly payments? If 7 years have passed, what would her loan balance be?

Answer 1

The value of a bond can be calculated using the present discounted value of its future cash flows. If the discount rate is 8%, equivalent to the coupon rate, the bond's present value equals its face value, $3,000. When the discount rate increases to 11%, the bond's value decreases to $2,847.44 due to the higher present discount applied to future cash flows.

Step-by-step explanation:

To determine the value of an investment like a bond, we need to calculate the present discounted value of its future cash flows. The present value of a bond is the sum of the present values of all future cash flows, discounted back at the interest rate or discount rate. For simplicity, let's take a two-year bond with a face value of $3,000 and a coupon rate of 8%. This bond pays annual interest, which means it will pay $240 in interest each year ($3,000 x 0.08), and at the end of the second year, it will also pay back the principal amount of $3,000.

If the discount rate is equal to the coupon rate (8%), the bond is worth its face value because the present value of its future cash flows equals the amount paid for it. When using an 8% discount rate, you receive $240 after the first and second years, which have present values of $222.22 and $205.76 respectively, and the principal of $3,000 in the second year, which has a present value of $2,777.78. So the total present value at an 8% discount rate is the sum of these figures, rounding to the nearest dollar, which equals the face value of $3,000.

Should interest rates rise, causing the discount rate to increase to 11%, the bond's present value will decrease. The reason is that the future cash flows are now discounted more heavily. For instance, at an 11% discount rate, the present value of the two $240 interest payments would be $216.22 and $194.80 respectively, and the present value of the $3,000 principal would be $2,436.42, giving a total present valued amount of $2,847.44.

These examples illustrate how the value of fixed-income investments like bonds can fluctuate with changes in interest rates, causing the bond prices to move inversely to the yield – when interest rates go up, bond prices go down, reflecting the higher opportunity cost of capital.