Asteroid Systems (J08) and Phobos Co (D08)

Asteroid:

It is the % change in the midpoint. So for 1 month it is ((1.6242 – 1.6223) / 1.6242) x 12
For 3 months it is ((1.6242 – 1.6176) / 1.6242) x 4

(Although I would not worry about this particularly – it has only happened once and it was the previous examiner. I do not think the new examiner would do this.)

Phobos:

The lock-in rate is 93.88 + 0.04 = 93.92, which is equivalent to 6.08%, plus 50 basis points = 6.58% (which is the same as the annual equivalent, which is 6.58% (not 5.68%)).
(Alternatively, the lock-in rate is 94.00 – 0.08 = 93.92 – either way always gives the same answer)

Since they are borrowing money, the would want the effective rate to be as low as possible.

On its own maybe, but there is also the premium to take into account. You wrote yourself that the effective rate is lower for 94000 at 5.63%

The answer is in fact very poor for several reasons.

One is that looking at an average interest rate is meaningless.

If they do choose an exercise price of 94.00 then the effective interest rate will be either 6.63% or 5.67% depending on whether the interest goes up or down.

The answer should also have considered an exercise price of 94.25 as well, in which case the effective interest would be either 6.51% or 5.55%,

It is not really possible to say which is better because although on the one hand 94.25 gives a lower maximum interest, it costs more in premium and if interest rates were to fall by more than 1% (say 2% or 3%) then neither option would be exercised but more premium would be payable with an exercise price of 94.25.

However, one terribly important thing that the answer does not mention is the aim stated in the question of keeping the effective interest below 6.6%. An exercise price of 94.25 will achieve that, whereas 94.00 will not quite achieve it if interest rates go up.