# Reconciling RNOA with ROCE by XNWk4d6R

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Reconciling RNOA with ROCE
Suggested Solution

data:
97                  96
Operating Assets                    3,000               2,600
Operating Liabilities               (1,100)             (1,000)
Debt (Interest bearing)             (1,400)             (1,200)
Common Shareholders=                  500                 400
Equity

Operating Earnings (BT)              224
Financial Expense (BT)               (104)
Tax Expense                           (30)
Net Earnings                           90

The statutory tax rate equals 35%.

Part A
(i)     Determine the effective tax-rate. Provide some reasons why the statutory and effective tax-rates may differ.

Effective tax rate: 30/(90+30) = 25%

The difference may be due to:
\$ Foreign operations
\$ Tax-privileged domestic transactions such as R&D or Puerto Rico
operations
\$ Reversal of tax reserves

(ii)    Determine capital contributions, net of dividends.

Net div=s = Net Income - CSE
=      90   - (500 - 400)
= -10

(This answer assumes that Net Income = Comprehensive Income)

(iii) Determine ROCE; use average CSE in the denominator.

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ROCE = 90/450 = 20%
(iv)   Determine RNOA; use average NOA in the denominator.

Operating Earnings (AT) = 90 + .65 x 104 = 157.6

[ (1,400 + 500) + (1,200 + 400) ]
Average NOA =                                                 = 1,750
2

RNOA = 9%

(v)    Reconcile ROCE and RNOA using the formula ROCE = RNOA + leverage x [RNOA - Borrowing Cost (AT)]

RNOA = 9%; see (iv)

Av . Debt 1,300
Leverage =              =      = 2.89
Av . CSE 450

Int . Exp .(AT) .65 x 104
BC(AT) =                     =          = 5.2%
Av . Debt       1,300

Hence
9% + 2.89 x [9% - 5.2%] = ROCE = 20%

(vi)   Assume WACC equals 10%. What is your best estimate of the cost of equity capital?

WACC = 10%

Leverage = 2.89

BC(AC) = 5.2%

CEC = WACC + Leverage x [WACC - BC(AT)]
= 10% + 2.89 x [10% - 5.2%]
= 23.87%

(vii) Is the company profitable?

No; RNOA < WACC (and ROCE < Cost of Equity Capital)

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Part B
Repeat with the following information:
97                96
Operating Assets                       3,000              2,600
Marketable Securities                  1,000              1,000
Operating Liabilities                  (1,100)           (1,000)
Common Shareholders= Equity             2,900              2,600

Operating Earnings (BT)                 315
Financial Revenue                        60
Tax Expense                             (100)
Net Earnings                             275

Note: In answering part (v), replace Aborrowing cost (AT)@ with Areturn on M/S (AT)@; also, leverage is now negative rather
than positive.

(i)        Effective tax rate: 100/375 = 26.7%

(ii)       Net div=s = 275 - 300
= -25

(iii) ROCE = 275/2,750 = 10%

(iv)
275 - .65 x 60    236
RNOA =                             =       = 13.5%
1,750         1,750

1,000
(v)        ROCE = 13.5 -                   x [13.5 - 3.9] = 10%
2,750

1,000
(vi) Cost of Equity = 10.0 -                     x [10.0 - 3.9] = 7.78
2,750

(vii)      Yes; RNOA > WACC and ROCE > Cost of Equity

Part C
Which of the two cases, A or B, shows the higher profitability?

Even though ROCE(A) > ROCE(B), it makes sense to say that B is more profitable

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than A. This claim is appropriate since only B exceeds its benchmark(s). Further
note that RNOA(B) > RNOA(A), and WACC(B) = WACC(A).

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