Market value of debt

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+K_d)^t)))/K_d]+[FV/((1+K_d)^t)]

• C = total interest expense.
• K_d = current cost of debt as a percentage.
• t = weighted average maturity of all debts in years.
• FV = total value of debt for the company.

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Market value of debt using 3M, an example:

C = total interest expense.

Total interest expense as found on the income statement is 0.529 billion.

K_d = current cost of debt as a percentage.

The cost of debt is the average interest the company pays on all of its loans.

Cost of debt = total interest / total debt

• Total interest = interest expense / (long term + short term debt)
  • Interest expense is 0.529 billion, found on the income statement.
  • Long term debt is 17.989 billion found on the balance sheet.
  • Short term debt is 7.948 billion shown as [total] current liabilities on the balance sheet.
  • Total interest = 0.529 / (17.989 + 7.948) = 0.02039.. or 2.03%.
• Total debt = short term + long term debt = 7.948 + 17.989 = 25.937 billion.

Cost of debt (K_d) = 2.03 / 25.937 = 0.0782... or 7.85%.

t = weighted average maturity of all debts in years

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 take a debt which is 367 million and matures in 2021
• Percentage of total = debt amount / total debt amount = 367/18783 = 0.01953 or 1.95%.
• Years to maturity = year debt matures - current year = 2021 - 2020 = 1
• For this one debt we have = percentage of total x years to maturity = 0.01953 * 1 = 0.01953

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

FV = total value of debt for the company

The total value of debt, or total liabilities found on the balance sheet, is 34,413 billion.

We can now work out the market value of debt

• C = 0.529
• K_d = 7.85%
• t = 10.94
• FV = 34,413

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

Final thoughts

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.

References

Richard J. Sweeney, Arthur D. Warga, and Drew Winters - The Market Value of Debt, Market Verses Book Value of Debt, and Returns to Assets.