You change one spreadsheet cell from 9% to 8%, and its valuation of Harbor Coffee jumps. No extra coffee sold. No new shop opened.
Our fictional coffee business's cash forecast has stayed still. Only the return demanded for owning that cash has moved.
Before accepting the higher number, ask where the rate came from and whose cash you are discounting. Correct arithmetic with the wrong rate still gives the wrong valuation.
Start with the alternative
Your $200 has other places to go. A required return is the return you could expect elsewhere for comparable risk. Wanting to earn 15% does not make 15% the company's cost of capital.
Harbor's forecast is in nominal US dollars: amounts that include expected inflation. Its rate needs the same currency and inflation basis. A long-lived business also needs a long-term risk-free benchmark, such as a US Treasury bond yield. A cash account's yield can reset long before the business stops earning.
In this teaching case, use a 5% benchmark, a 6% market equity premium, and a 6% pre-tax borrowing cost.
Estimate the equity return
Cost of equity is the return shareholders require for the risk they take. The capital asset pricing model, or CAPM, estimates it by scaling the market premium with beta, the stock's sensitivity to market returns.
Harbor's supplied beta estimate is 0.7. Its equity premium is 0.7 × 6% = 4.2 percentage points. Add the 5% benchmark: 5% + 4.2% = 9.2%.
That 6% is the whole market's premium. Beta has already scaled it for Harbor; adding another 6% for “company risk” would count it again.
CAPM prices market exposure; beta is not a complete inventory of business risk. The 9.2% is a required return, not a promise of what your shares will earn.
Blend debt and equity
Cost of debt is the return lenders require on new borrowing at the valuation date. Last year's interest expense divided by debt tells you about past financing, not the price of borrowing afresh.
Use Harbor's 25% teaching tax rate, with the full interest deduction usable. Each dollar of interest then saves 25 cents in tax. The after-tax debt cost is 6% × (1 − 25%) = 4.5%.
The weighted average cost of capital (WACC) blends equity and debt costs using market values. A larger share of the financing gets a larger weight.
At FY3 year-end, Harbor has 50 million shares at $66 each: $3,300 million of equity market value. Its interest-bearing debt totals $300 million. For this model, book debt stands in for market debt, and the weights stay fixed. Cash is not deducted from these financing weights.
- Equity weight: 3,300 ÷ 3,600 = 91.67%.
- Debt weight: 300 ÷ 3,600 = 8.33%.
That gives 91.67% × 9.2% + 8.33% × 4.5% ≈ 8.81%. We round the result to 9% for the working model. Because equity supplies most of the financing, WACC stays close to the equity cost.
Match the rate to the cash
The cash-flow match decides which rate belongs in the model:
- WACC: cash after taxes on operating profit and reinvestment, before interest and debt payments. It is available to lenders and shareholders together.
- Cost of equity: cash left for shareholders after taxes, reinvestment, interest and debt repayments, including cash from new borrowing.
Harbor has two rates because we can measure its cash for two different groups of investors.
Use a range you can explain
Keep the benchmark, beta, debt cost, tax and weights fixed. A 5% market premium gives WACC of about 8.17%; 6% gives 8.81%; 7% gives 9.45%.
We carry 8%, 9% and 10% forward, rounding the endpoints outward to leave room for errors in the debt proxy and other estimates. This is a range to test, not a measured probability band.
A desired stock price has no place among the inputs. The 9% now has a reason; the range shows how much the valuation depends on it.
Optional: change only the rate
The base operating forecast produces $171.69 million of cash before financing at the end of F5, five years after FY3. Keep that payment and its date fixed.
At 9%, its value at FY3 year-end is $171.69 million ÷ 1.09⁵ ≈ $111.59 million. The bars change only the rate.
At 8%, this one payment is worth $10.24 million more than at 10%. The extra value came entirely from the rate.
What would change the rate?
Harbor's rate note fits in one sentence: value nominal USD cash at FY3 year-end, place annual payments at each year-end, and use 8–10% WACC for cash available to lenders and shareholders together.
For a real company, each input needs evidence:
| Input | Value | Status | Evidence needed |
|---|---|---|---|
| Benchmark | 5% | Choice | Dated long-term yield |
| Market premium | 6% | Choice | Method and date |
| Beta | 0.7 | Cast estimate | Risk basis |
| Debt cost | 6% | Choice | Borrowing yield |
| Tax | 25% | Cast | Usable tax saving |
| Equity / debt | 91.67% / 8.33% | Derived | Market values |
Source: Harbor's FY3 cast figures and the choices above.
The market premium is the main unresolved estimate tested here. A different premium changes the rate even if Harbor's shops sell exactly the same amount of coffee. Without evidence to narrow the range, more decimal places add digits without adding knowledge. Discounted cash flow applies these rates to the full forecast.
In short
- Required return is grounded in alternatives with comparable risk, not a personal wish.
- Cost of equity discounts shareholder cash; WACC discounts cash for lenders and shareholders together.
- Harbor's inputs give 8.81% WACC, rounded to a 9% working rate.
- A rate range tests your judgment; it does not prove the answer is inside it.