The market value of debt is an estimate of the market value of a company's debt. Put another way, it is the price at which the market is willing to buy a company's debt. Calculating the market value of debt is tricky and requires a lot of inputs. All inputs may not always be available on a company's quarterly or annual reports, however, in this article we will look at 3M's annual report which does list all required inputs. 3M's annual report can be found here.
Market Value of Debt = C[(1–(1/((1+Kd)t)))/Kd]+[FV/((1+Kd)t)]
Total interest expense as found on the income statement is 0.529 billion.
The cost of debt is the average interest the company pays on all of its loans.
Cost of debt = total interest / total debt
Cost of debt (Kd) = 2.03 / 25.937 = 0.0782... or 7.85%.
The weighted average maturity (WAM) of 3M's debt is tricky to work out. Page 88 of the annual report lists the long term debt including the amount (in millions), the effective interest rate and the maturity date. Consider that we have three bonds, bond A, bond B and bond C. To calculate the WAM we use the following formula:
WAM = (bond A percentage of total x bond A years to maturity) + (bond B percentage of total x bond B years to maturity) + (bond C percentage of total x bond C years to maturity)
The long term debt table on page 88 gives us the amount (shown as carrying value), interest rate and maturity date of each debt as well as the total amount of debt. For each debt row we need to calculate its percentage of total and its years to maturity. To look at an example:
We then need to repeat this calculation for each debt row in the table and add them together. This calculation is fairly trivial to do in a spreed sheet but for convenience the results of the calculations are shown below.
| Amount | Maturity date | Years to maturity | Percent of total | Percent x years to maturity |
|---|---|---|---|---|
| 374 | 2021 | 1 | 2.00% | 0.02 |
| 367 | 2021 | 1 | 1.96% | 0.02 |
| 612 | 2022 | 2 | 3.27% | 0.07 |
| 598 | 2022 | 2 | 3.20% | 0.06 |
| 449 | 2022 | 2 | 2.40% | 0.05 |
| 731 | 2023 | 3 | 3.91% | 0.12 |
| 649 | 2023 | 3 | 3.47% | 0.10 |
| 498 | 2023 | 3 | 2.66% | 0.08 |
| 299 | 2024 | 4 | 1.60% | 0.06 |
| 299 | 2024 | 4 | 1.60% | 0.06 |
| 502 | 2024 | 4 | 2.68% | 0.11 |
| 548 | 2025 | 5 | 2.93% | 0.15 |
| 744 | 2025 | 5 | 3.98% | 0.20 |
| 498 | 2025 | 5 | 2.66% | 0.13 |
| 908 | 2026 | 6 | 4.85% | 0.29 |
| 644 | 2026 | 6 | 3.44% | 0.21 |
| 843 | 2027 | 7 | 4.51% | 0.32 |
| 225 | 2028 | 8 | 1.20% | 0.10 |
| 598 | 2028 | 8 | 3.20% | 0.26 |
| 796 | 2029 | 9 | 4.25% | 0.38 |
| 986 | 2029 | 9 | 5.27% | 0.47 |
| 604 | 2030 | 10 | 3.23% | 0.32 |
| 595 | 2030 | 10 | 3.18% | 0.32 |
| 608 | 2031 | 11 | 3.25% | 0.36 |
| 551 | 2037 | 17 | 2.94% | 0.50 |
| 96 | 2041 | 21 | 0.51% | 0.11 |
| 315 | 2044 | 24 | 1.68% | 0.40 |
| 53 | 2044 | 24 | 0.28% | 0.07 |
| 476 | 2046 | 26 | 2.54% | 0.66 |
| 492 | 2047 | 27 | 2.63% | 0.71 |
| 637 | 2048 | 28 | 3.40% | 0.95 |
| 505 | 2048 | 28 | 2.70% | 0.76 |
| 969 | 2049 | 29 | 5.18% | 1.50 |
| 642 | 2050 | 30 | 3.43% | 1.03 |
| 18,711 | 100% | 10.94 |
NOTE: totals are shown in the last row. The 'percent of total' and 'percent x years to maturity' values are rounded up to two decimal places.
t (WAM) = 10.94
The total value of debt, or total liabilities found on the balance sheet, is 34,413 billion.
Market value of debt = 0.5299*((1-(1/((1+0.0785)10.94)))/0.0785)+(34413/((1+0.0785)10.94))
Market value of debt = 15.058 billion
Market value of debt appears to be a better measure of a company's debt than just using the book value of debt for calculations such as the weighted average cost of capital (WACC). Sweeney et al. found, by performing test calculations using both book value and market value of debt that results diverged substantially (when examining a cross-section of the market). Book values of debt tend to give less accurate results than market value of debt.
Richard J. Sweeney, Arthur D. Warga, and Drew Winters - The Market Value of Debt, Market Verses Book Value of Debt, and Returns to Assets.
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