what would be the present value of the tax shield?

Question

The management of Graphicopy is trying to determine how much debt they should have in their capital structure. If they sell $500,000 in perpetual bonds with a 9 percent coupon, what would be the present value of the tax shield? Assume the marginal tax rate is 35%.
a.$15,750
b.$29,250
c.$175,000
d.$45,000

Answer 1

The PV of the tax shield on a perpetual bond is equal to the tax rate times the amount of the bond -- so C is the correct answer. This answer assumes that they sell the bond for the face value of $500,000

How do we get this?

Every year, there is an interest payment of 9% -- or $45,000. This is an expense -- so you deduct it from EBIT (ernings before interest and taxes). That means you don't have to pay taxes on it, so you are shielding the tax on $45,000. This is 35% of $45,000 or $15,750.

This happens every year -- forever. This means that the tax shield is a $15,750 perpetuity. You should have learned how to find the PV of a perpetuity. It is:

PV = C/r

where 'C' is the cash flow and 'r' is the appropriate discount rate. The appropriate discount rate here is the cost of debt -- which is 9%. This means that the PV of the tax shield is:

PV = $15,750 / 0.09 = $175,000

While this is the usual convention for computing the value of the tax shield, it is actually slightly overstated. The discount rate reflects the possibility of losing the tax shield if the company defaults (it is built into the 9%) -- but it does not reflect the possibility that there may be years when the company does not make money but does not default (therebye losing the tax shield during those years). Consequently, the tax shield is actually worth slightly less at issuance.

Answer 2

Tax Shield

Answer 3

You need to figure out what your present amount is the amount today. What the future amount is on the last day, and any intermitten amounts. I am assuming you have a financial calculator since you are doing a problem like this. There are four keys on the calculator that will calulate the value if you input into them. i/y, n, pv, fv etc. and compute [cpt] for the missing variable. Hope this gets you started, I won't work the problem for you.

Answer 4

it's been awhile since i did this, but i believe the answer is c. $175, 000.

the tax shield the interest payments times the tax rate. so 9% times $500,000 = $45,000. which times 35% = $15,750, which capitalized at 9% equals $175,000.

i think that's your answer, but agian, i haven't done this since college 8 years ago.