Podcast Beta
Questions and Answers
What is the present value of $100 expected two years from today at a discount rate of 6%?
What is present value defined as?
If the annual interest rate is 12.00%, what is the two-year discount factor?
If the present value of cash flow X is $240, and the present value of cash flow Y is $160, then the present value of the combined cash flows is:
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The rate of return is also called the:
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What is used as a measure of a bond’s interest rate risk or sensitivity to a change in its yield?
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How is modified duration (ModDur) calculated?
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When is a bond sold at a premium?
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How is Macaulay duration (MacDur) calculated?
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What does a bond's annual Macaulay duration represent?
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What is used as a measure of a bond’s interest rate risk or sensitivity to a change in its yield?
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How is modified duration (ModDur) calculated?
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When is a bond sold at a premium?
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What does a bond's annual Macaulay duration represent?
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If the present value formula is used to value bonds, what does CR represent when the bond is sold at par?
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Study Notes
Present Value and Discount Rates
- Present value (PV) calculates the worth of future cash flows today, accounting for a specific discount rate.
- PV of $100 expected two years from now at a 6% discount rate is approximately $89.00.
- Present value formula: ( PV = \frac{FV}{(1 + r)^n} ) where ( FV ) is future value, ( r ) is the discount rate, and ( n ) is the time in years.
Discount Factors
- For an annual interest rate of 12.00%, the two-year discount factor is approximately 0.7972.
- Discount factor formula: ( DF = \frac{1}{(1 + r)^n} ).
Combined Present Values
- Present value of cash flow X is $240 and cash flow Y is $160; combined present value becomes $400.
Rate of Return Terminology
- The rate of return is also known as the yield.
Bond Interest Rate Sensitivity
- A bond’s interest rate risk or sensitivity to changes in yield is measured by duration.
- Modified duration (ModDur) indicates the percentage change in price for a 1% change in yield.
Modified Duration Calculation
- Modified duration is calculated as ( \text{MacDur} / (1 + r) ) where MacDur is Macaulay duration.
Premium Bonds
- A bond sells at a premium when the market interest rates are lower than the bond’s coupon rate.
Macaulay Duration
- Macaulay duration (MacDur) is the weighted average time until cash flows are received.
- A bond's annual Macaulay duration represents the time value of cash flows, enabling investors to assess interest rate sensitivity.
Bond Valuation
- In bond valuation at par, CR represents the coupon rate, equalling the market rate.
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Description
Test your knowledge of present value and discounting with this quiz. Answer questions on calculating present value, discount rates, and interest rates.
