25556 Chap.3 Leverage, Yield, Liquidity and Time Value of Money
Leverage, Yield, Liquidity and Time Value of Money
The Topic 1 workshop gathers six ideas that every later calculation in the subject relies on: the two forms of finance, leverage, return, liquidity, risk and the time value of money. Debt promises interest and repayment and can force a firm into liquidation; equity buys part-ownership, votes and dividends with no promise of repayment.
Leverage, the use of debt, lifts the return on equity when business is good and deepens losses when it is not.
The chapter shows that trade-off on a graph, then turns returns into comparable annual figures with the simple interest yield on a 365-day year.
It explains why investors demand a liquidity premium for money they cannot easily reach and a risk premium on top of the risk-free rate, and it uses present value to show what that premium costs an issuer in today's dollars.
What this chapter covers
- 01
Debt and equity as the two forms of finance
- 02
Leverage, the debt-to-equity ratio and return on equity
- 03
Interest, dividends and capital gains as returns
- 04
The simple interest yield on a 365-day year
- 05
Liquidity and the liquidity premium
- 06
Risk premiums and present value
Worked example · free
Discount a three-year $50,000 payment at a risk-free rate and with a risk premium
- 1Risk-free value: $50,000 ÷ 1.04³ = $50,000 ÷ 1.124864 = $44,449.82.
- 1Required rate with the premium: 4% + 3% = 7%, so the value is $50,000 ÷ 1.07³ = $50,000 ÷ 1.225043 = $40,814.89.
- 1Cost of the premium: $44,449.82 − $40,814.89 = $3,634.92 less raised today for the same promise.
- 1Rate for a $42,000 value: (50,000 ÷ 42,000) raised to the power 1/3, minus 1, gives 5.98% p.a., which lies between the two rates as it should.
Key terms
- Leverage
- Borrowing to finance a business or an investment, usually gauged by the debt-to-equity ratio.
- Return on equity
- Net profit after tax divided by shareholders' equity, the return earned on the owners' funds.
- Simple interest yield
- A holding-period return scaled to an annual rate without compounding, using 365 days in the year.
- Liquidity
- How easily an investor can turn a holding back into money at a fair market value.
- Risk premium
- The extra return above the risk-free rate that risk-averse investors require before accepting risk.
- Present value
- What a future payment is worth today once it is discounted at the required rate of return.
Leverage, Yield, Liquidity and Time Value of Money FAQ
Why does leverage increase return on equity?
Debt usually costs less than the return the firm earns on its assets, so profit left after paying interest is spread over a smaller equity base. That lifts return on equity when earnings are healthy. The same arithmetic works in reverse: when earnings fall below the cost of the debt, the levered firm's owners lose more than an all-equity firm's would.
How do you calculate a simple interest yield?
Divide the amount received by the amount paid, subtract one to get the return over the holding period, then multiply by 365 and divide by the number of days held. For example, paying $9,800 and receiving $10,000 after 73 days gives a return of about 2.04% for the period, or roughly 10.2% a year.
What is the difference between a risk premium and a liquidity premium?
A risk premium compensates the investor for the chance of receiving less than expected, such as a default. A liquidity premium compensates for money that cannot quickly be turned back into cash at fair value, such as an investment in property. A single security can carry both.
Why is a future payment worth less than the same amount today?
Investors want a return for waiting, so money promised later must be discounted back at the required rate. The higher that rate, because of risk or illiquidity, the lower the present value, which is how the subject compares cash flows arriving at different dates.
Is time value of money taught again in this subject?
The workshop treats time value of money skills from the earlier finance subject as assumed knowledge, so expect to apply present and future value calculations without a full refresher. Revise compounding, discounting and annuities early, because loans, deposits and bonds all build on them.
Exam move
Start by redrawing the leverage graph from scratch: pick an asset total, a debt share and an interest rate, compute return on equity at two profit levels for each firm, and find where the lines cross. Then practise the simple interest yield until the 365-day convention is automatic, comparing holdings of different lengths.
For present value, build a small table of one future payment discounted at three rates and note how quickly value falls as the premium grows. Finish by writing one sentence that links leverage, risk, liquidity and the discount rate, since that link ties the four ideas together.
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