The market value of Firm L’s debt is $200,000 and its cost of debt is 7%. The firm’s equity has a market value of $400,000, its earnings are growing at a 4% rate, and its tax rate is 40%. A similar firm with no debt has a cost of equity of 12%. Use the APV model to calculate the value of Firm L if it had no debt.

$530000

Explanation:

Debt $200000.

Equity $400000

rd=7%.

rd for equity =12%

Taxrate= 40%

Earning rate for equity= 4%

Firm L has a total of $200000+ $400000= $600000

A similar firm with no debt should have a smaller value.

The calculation is as follows.

VTotal= Vu + Vts

Make Vu the subject of the formula

So,

Vu= VTotal - Vts

= Debt + Equity(S) - Vts

Firstly, we need to calculate Vts

Value tax shelter (Vts)

=rdTD(rsU-G)

= 0.07(0.40)(200000)/(0.12-0.04)

=5600/0.08

= $80,000

Therefore,

Vu= $200000 + $400000- $70000

Vu= $600000 - $70000

Vu= $ 530000

In conclusion

The value of Firm L if it has no debt is $530000

$530,000

Explanation:

Debt: $200,000

rd: 7%

T: 40%

Equity: $400,000

rsU: 12%

g: 4%

Firm L has a total value of $200,000 + $400,000 = $600,000. A similar firm with no debt should therefore have a smaller value.

VTotal= VU+ VTS

Therefore VU= VTotal−VTS= D + S −VTS.

Value tax shelter = VTS= rdTD/(rsU−g)

= 0.07(0.40)($200,000)/(0.12 −0.04)

=$5,600/0.08

= $70,000

VU= $400,000 + $200,000 −$70,000

$600,000-$70,000 = $530,000

VU= $530,000

The value of Firm L if it had no debt is $530,000