It will be 45 weeks until the album sells fewer than 2000 copies.
We can look at the equation (0.96)^x = 2000/12400 to find the number of weeks, x, that the 4 percent reduction will yield the ratio of sales endpoint to sales now. We can solve the equation by taking a log of both sides in order to isolate the x variable. Using the natural log, we'd have x*ln(0.96) = ln(2000/12400). Solving this shows x to be ~=44.69525, so we round up to 45 weeks. We can confirm our solution by verifying that 0.96^45 is indeed less than 2000/12400. (0.159.. < 0.161...)
Answer:
(a) 15.46%
(b) $11,904.11
(c) 6.15%
Explanation:
(a) Sustainable growth rate:
= 29.32%
Retention Ratio = 1 - Dividend Payout
= 45.66%
= 0.15446
= 15.46%
(b) Additional borrowing:
New Total Asset = (Total debt + Total equity) × (1 + Sustainable growth rate)
= (77,000+59,000) × (1 + 15.46%)
= 157025.4
= $88904.11
Increase in Borrowing = New debt - old debt
= $88,904.11 - $77,000
= $11,904.11
(c) Internal growth rate:
= 12.72%
= 0.0615
= 6.15%