Question

BTC Corporation is in big trouble. It recently sold off its tangible assets because it could not operate its business profitably. BTC’s only remaining asset is $2 million in cash. Unfortunately, BTC previously issued bonds with a face value of $3 million.

(a) If BTC were to be liquidated immediately, what would be the amounts paid to the bond holders and to the stockholders, respectively?

(b) BTC’s managers (who are also the stockholders) are considering using the $2 million in cash to fund a risky investment.   In exchange for investing the $2 million, BTC would immediately receive either $3.8 million or $0, with equal probability. What is the NPV of this proposed investment? (Use a zero discount rate).

(c) Assume that BTC commits to making this investment, but that the outcome is not yet known. BTC would be liquidated as soon as the outcome was known. What is the market value now of BTC’s stock and of its bonds? (Continue to use a zero discount rate).

(d) Explain the principle illustrated here.   

Answer 1

(a) If BTC were to be liquidated immediately, what would be the amounts paid to the bond holders and to the stockholders, respectively?

Total assets, A = $ 2 mn of cash

Face value of bonds, F = $ 3 mn

Amounts to be paid to bond holders, D = min (A, F) = min (2, 3) = $ 2 mn

Amounts to be paid to stockholder = max (A - D, 0) = max (2 - 2, 0) = 0

(b) BTC’s managers (who are also the stockholders) are considering using the $2 million in cash to fund a risky investment.   In exchange for investing the $2 million, BTC would immediately receive either $3.8 million or $0, with equal probability. What is the NPV of this proposed investment? (Use a zero discount rate).

NPV_upside = -C₀ + C₁ = - 2 + 3.8 = $ 1.8 mn

NPV_downside = -2 + 0 = -$ 2 mn

Each has equal probability of 0.5

Hence, expected NPV = 0.5 x 1.8 + 0.5 x (-2) = - $ 0.1 mn

(c) Assume that BTC commits to making this investment, but that the outcome is not yet known. BTC would be liquidated as soon as the outcome was known. What is the market value now of BTC’s stock and of its bonds? (Continue to use a zero discount rate).

In case of upside, Asset value, A = $ 3.8 mn

Hence, bonds value, D = min (A, F) = min (3.8, 3) = $ 3 mn

And equity value = max (A - D, 0) = max (3.8 - 3, 0) = $ 0.8 mn

In case of downside, Asset value, A = 0

Hence, bonds value, D = min (A, F) = min (0, 3) = 0

And equity value = max (A - D, 0) = max (0 - 3, 0) = 0

Each scenario has a equal probability of 0.5

Hence, market value of bonds = 0.5 x 3 + 0.5 x 0 = $ 1.50 mn

and market value of equity = 0.5 x $ 0.8 mn + 0.5 x 0 = $ 0.4 mn

(d) Explain the principle illustrated here.   

The principle illustrated here is that of conflict between shareholders and bondholders. This is also known as agency problem. In case of distress, the shareholders, who anyways are the last ones to get paid, intends to undertake risky project with a hope that a miraculously high rewards (returns) can help them pay off everyone else above them in the pecking order and still some residual cash flows are left for them. This is the only way they can get some money from the corporation in case of distress. Bondholders think differently. They intend to undertake safer, stable and mature cash flows, so they prefer less riskier projects, so that uncertainty is reduced and they get paid.