Multiple Choice
What is the total interest due at maturity on a \$1,500, 12\% annual interest rate, 120-day note? (Assume a 360-day year and simple interest.)
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10. Time Value of Money
Time Value of Money Equations
Multiple Choice
All else held constant, the present value of a bond increases when the:
A
future cash flows decrease
B
time to maturity increases
C
coupon payments decrease
D
discount rate decreases
Verified step by step guidance1
Step 1: Understand the concept of present value (PV) of a bond. The present value is the current worth of future cash flows (coupon payments and principal repayment) discounted at a specific rate, known as the discount rate. The formula for PV is: PV = Σ (CF / (1 + r)^t), where CF represents cash flows, r is the discount rate, and t is the time period.
Step 2: Analyze the relationship between the discount rate and the present value. When the discount rate decreases, the denominator in the formula (1 + r)^t becomes smaller, which increases the value of each discounted cash flow. This leads to a higher present value for the bond.
Step 3: Consider the other factors mentioned in the problem. If future cash flows decrease, the numerator in the formula (CF) becomes smaller, reducing the present value. Similarly, if coupon payments decrease, the cash flows decrease, leading to a lower present value. If the time to maturity increases, the cash flows are discounted over a longer period, which can reduce the present value depending on the discount rate.
Step 4: Focus on the correct answer provided: 'discount rate decreases.' This is the key factor that directly increases the present value of a bond, as explained in Step 2.
Step 5: Summarize the reasoning: The present value of a bond increases when the discount rate decreases because the cash flows are discounted at a lower rate, making them more valuable in today's terms.
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