Respuesta :
Answer:
(a) 15.46%
(b) $11,904.11
(c) 6.15%
Explanation:
(a) Sustainable growth rate:
[tex]Return\ on\ equity\ (ROE)=\frac{Net\ income}{Total\ equity}[/tex]
[tex]Return\ on\ equity\ (ROE)=\frac{17,300}{ 59,000}[/tex]
= 29.32%
Retention Ratio = 1 - Dividend Payout
[tex]=1-[\frac{9,400}{17,300}][/tex]
= 45.66%
[tex]Sustainable\ growth\ rate=\frac{(ROE\times Retention\ Ratio)}{(1-ROE\times Retention\ Ratio)}[/tex]
[tex]Sustainable\ growth\ rate=\frac{(0.2932\times 0.4566)}{(1-0.2932\times 0.4566)}[/tex]
[tex]=\frac{0.1338}{0.8662}[/tex]
= 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
[tex]New\ Debt=\frac{D}{D+E}\times New\ Total\ Asset[/tex]
[tex]New\ Debt=\frac{77,000}{77,000+59,000}\times 157024.4[/tex]
= $88904.11
Increase in Borrowing = New debt - old debt
= $88,904.11 - $77,000
= $11,904.11
(c) Internal growth rate:
[tex]ROA=\frac{Net\ income}{Debt+equity}[/tex]
[tex]ROA=\frac{17,300}{77,000+59,000}\times 100[/tex]
= 12.72%
[tex]Internal\ growth\ rate=\frac{(ROA\times Retention\ Ratio)}{(1-ROA\times Retention\ Ratio)}[/tex]
[tex]Internal\ growth\ rate=\frac{(0.1272\times 0.4566)}{(1-0.1272\times 0.4566)}[/tex]
[tex]=\frac{0.0580}{0.942}[/tex]
= 0.0615
= 6.15%